DETAILED ACTION
Receipt of Applicant’s amendment filed 12/11/2025 is acknowledged.
Claims 10 and 14 have been amended.
Claim 13 has been canceled.
Claims 19, 20, and 21 have been added.
Claims 10-12 and 14-21 are pending.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Priority
Acknowledgment is made of applicant’s claim for foreign priority under 35 U.S.C. 119 (a)-(d). The certified copy has been filed in parent Application No. FR1914967, filed on 12/19/2019.
Examiner Notes
Examiner cites particular columns, paragraphs, figures and line numbers in the
references as applied to the claims below for the convenience of the applicant. Although
the specified citations are representative of the teachings in the art and are applied to
the specific limitations within the individual claim, other passages and figures may apply
as well. Examiner may also include cited interpretations encompassed within parenthesis, e.g. (Examiner’s interpretation), for clarity. It is respectfully requested that, in preparing responses, the applicant fully consider the references in their entirety as potentially teaching all or part of the claimed invention, as well as the context of the passage as taught by the prior art or disclosed by the examiner. The entire reference is considered to provide disclosure relating to the claimed invention. The claims & only the claims form the metes & bounds of the invention. Office personnel are to give the claims their broadest reasonable interpretation in light of the supporting disclosure. Unclaimed limitations appearing in the specification are not read into the claim. Prior art was referenced using terminology familiar to one of ordinary skill in the art. Such an approach is broad in concept and can be either explicit or implicit in meaning. Examiner's Notes are provided with the cited references to assist the applicant to better understand how the examiner interprets the applied prior art. Such comments are entirely consistent with the intent & spirit of compact prosecution.
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
Response to Arguments
Claim Rejections under 35 U.S.C. § 101:
Acknowledgement is made of amended independent claim 1. Applicants arguments filed 12/11/2025 have been fully considered, but are not persuasive. Rejections to claims 10-12 and 14-18 are maintained. New claims 19-21 are rejected.
Note: Applicant’s amendment necessitated the new ground(s) of rejection presented in this Office Action.
Applicant argues [Pg.1-2] amended independent claim 1 integrates into a practical application, recites significantly more than alleged abstract idea, and is a “technical improvement” to the “function and outcome of a computer software simulation” [Pg.2 Ln.6]. Examiner respectfully disagrees.
The steps of the subject matter eligibility analysis for products and processes that are to be used during examination for evaluating whether a claim is drawn to patent-eligible subject matter is the following:
Step 1: Determine if the claim is directed to a process, machine, manufacture, or composition of matter. Claims 10-12, 14-17 and 19-21 are directed towards a method, therefore fall within the statutory category of a process. As noted in Office Action dated 8/11/2025, claim 18 is directed towards software per se, and as such doesn’t fall within a statutory category.
Step 2A (Prong 1): Determine if the claim is directed to a law of nature, a natural phenomenon (product of nature), or an abstract idea. Independent claim 1 is directed towards an abstract idea (Mental Processes and/or Mathematical Concepts) – see Claim Rejections - 35 USC §101 section below for detailed analysis.
Step 2A (Prong 2)/Step 2B: Determine if the claim recites additional elements that amount to significantly more than the judicial exception. As shown in 35 USC §101 analysis section below, the additional elements as described in Step 2A Prong 2 are not sufficient to amount to significantly more than the judicial exception because the additional limitations are considered Mere Instructions to Apply an Exception per MPEP 2106.05(f). The additional claim limitations identified in Claim 1 can be summarized as mere instructions to implement an abstract idea (i.e. mental processes and/or mathematical concepts) on a generic computer. These additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea when considered as an ordered combination and as a whole. Per MPEP 2106.05(f), “implementing an abstract idea on a generic computer, does not integrate the abstract idea into a practical application in Step 2A Prong Two or add significantly more in Step 2B, similar to how the recitation of the computer in the claim in Alice amounted to mere instructions to apply the abstract idea of intermediated settlement on a generic computer.” Additionally, per MPEP 2106.05(f)(2), “examples where the courts have found the additional elements to be mere instructions to apply an exception, because they do no more than merely invoke computers or machinery as a tool to perform an existing process include... v. Requiring the use of software to tailor information and provide it to the user on a generic computer, Intellectual Ventures I LLC v. Capital One Bank (USA), 792 F.3d 1363, 1370-71, 115 USPQ2d 1636, 1642 (Fed. Cir. 2015).
Per MPEP 2106.05(d), another consideration when determining whether a claim recites significantly more than a judicial exception is whether the additional element(s) are well-understood, routine, conventional activities previously known to the industry. The courts have recognized the following relevant computer functions as well‐understood, routine, and conventional functions: i. Receiving or transmitting data over a network, ii. Performing repetitive calculations, iii. Electronic recordkeeping, iv. Storing and retrieving information in memory.
Since the additional elements are directed towards Mere Instructions to Apply an Exception, and have been determined to be well understood, routine, conventional activity per MPEP 2106.05(d), claim 1 is directed to an abstract idea without significantly more and is rejected as not patent eligible under 35 U.S.C. 101.
Similar rationale for rejection is provided for independent claims below.
Claim Rejections under 35 U.S.C. § 103:
Acknowledgement is made of amended independent claim 1, dependent claim 14, and the addition of claims 19-21. Applicants arguments filed 12/11/2025 have been fully considered, but are not persuasive. Rejections to claims 10-12 and 14-18 are maintained. New claims 19-21 are rejected under similar rationale.
Note: Applicant’s amendment necessitated the new ground(s) of rejection presented in this Office Action.
In response to applicant’s argument [Pg.4 P.1] that there is no teaching, suggestion, or motivation to combine the references (i.e. Li and Sun), the examiner recognizes that obviousness may be established by combining or modifying the teachings of the prior art to produce the claimed invention where there is some teaching, suggestion, or motivation to do so found either in the references themselves or in the knowledge generally available to one of ordinary skill in the art. See In re Fine, 837 F.2d 1071, 5 USPQ2d 1596 (Fed. Cir. 1988), In re Jones, 958 F.2d 347, 21 USPQ2d 1941 (Fed. Cir. 1992), and KSR International Co. v. Teleflex, Inc., 550 U.S. 398, 82 USPQ2d 1385 (2007).
In this case, Li teaches a deep domain decomposition method (D3M) based on the variational principle for PDEs. Li discloses “The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems.” [Abstract]. And Sun teaches a physics-constrained deep learning approach for surrogate modeling of fluid flows. Sun discloses “a structured deep neural network (DNN) architecture is devised to enforce the initial and boundary conditions, and the governing partial differential equations (i.e., Navier–Stokes equations) are incorporated into the loss of the DNN to drive the training” [Abstract]. Thus, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the computational efficiency of Li with the physics-informed neural networks of Sun in order to solve large-scale PDE based systems, such as fluid dynamics. Thus, Applicant’s argument isn’t persuasive.
Applicant also argues [Pg.4 P.2] the art of record fails to teach or render all of the limitations recited in each independent claim. Examiner respectfully disagrees. As can be seen in Claim Rejections – 35 USC 103 section below, the combination of Li and Sun disclose all recited limitations in claims 10-12 and 14-20. The combination of Li-Sun-Bhatnagar disclose the limitations recited in amended claim 20. Thus, Applicant’s argument isn’t persuasive.
Claim Objections
Claim 10 is objected to because of the following informalities:
Claim 10(b) states “by performing a computation step comprising”. This limitation is inaccurate since multiple computation steps are performed. Examiner recommends updating limitation to state “by performing computational steps comprising”.
Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 10 and 21 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Regarding claim 10(b), the claim recites “using a machine learning algorithm, predicting a global solution”. It is unclear if a machine learning algorithm is to be used for predicting a global solution or if the machine learning algorithm is to be used elsewhere. Claim 10(b) further recites “in the simulation domain, by performing a computation step”. It is unclear if “by performing a computation step” is referring to the “machine learning algorithm” or “predicting a global solution”. For purposes of compact prosecution, the Examiner interprets claim 10 (b) to mean “using a machine learning algorithm to predict a global solution to said at least one differential equation in the simulation domain by performing a computation step comprising”. Clarification is required.
Regarding claim 10(b)(ii)(B), the claim recites “using the machine learning algorithm, predicting a local solution”. It is unclear if a machine learning algorithm is to be used for predicting a local solution or if the machine learning algorithm is to be used elsewhere. For purposes of compact prosecution, the Examiner interprets claim 10 (b)(ii)(B) to mean “using the machine learning algorithm to predict a local solution”. Clarification is required.
Regarding claim 21, the terms “of about 50%” and “of about 25%” in claim 21 are relative terms which renders the claim indefinite. The terms “of about” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. For purposes of compact prosecution, the examiner interprets “of about 50%” to be a range between 40-60% and “of about 25%” to be a range between 20-30%. Clarification is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 10-12 and 14-21 are rejected under 35 U.S.C. 101 because the claimed invention recites a judicial exception, is directed to that judicial exception (an abstract idea), as it has not been integrated into a practical application and the claim(s) further do/does not recite significantly more than the judicial exception. Examiner has evaluated the claim(s) under the framework provided in MPEP 2106 and has provided such analysis below.
To determine if a claim is directed to patent ineligible subject matter, the Court
has guided the Office to apply the Alice/Mayo test, which requires:
Step 1. Determining if the claim falls within a statutory category of a Process, Machine, Manufacture, or a Composition of Matter (see MPEP 2106.03);
Step 2A. Determining if the claim is directed to a patent ineligible judicial exception consisting of a law of nature, a natural phenomenon, or abstract idea (MPEP 2106.04);
Step 2A is a two-prong inquiry. MPEP 2106.04(II)(A).
Under the first prong, examiners evaluate whether a law of nature, natural phenomenon, or abstract idea is set forth or described in the claim. Abstract ideas include mathematical concepts, certain methods of organizing human activity, and mental processes. MPEP 2106.04(a)(2).
The second prong is an inquiry into whether the claim integrates a judicial exception into a practical application. MPEP 2106.04(d).
Step 2B. If the claim is directed to a judicial exception, determining if the claim recites limitations or elements that amount to significantly more than the judicial exception. (See MPEP 2106).
Step 1:
Claims 10-12, 14-17 and 19-21 are directed to a method, as such these claims fall within the statutory category of a process.
Claim 18 is directed towards software per se, and as such doesn’t fall within a statutory category. MPEP 2106.03 - Products that do not have a physical or tangible form, such as information (often referred to as "data per se") or a computer program per se (often referred to as "software per se") when claimed as a product without any structural recitations. Note: Claim 18 has also been addressed under the abstract idea analysis below.
Step 2A, Prong 1:
The examiner submits that the foregoing claim limitations constitute abstract ideas, as the claims cover Mental Processes and/or Mathematical Concepts, given the broadest reasonable interpretation.
In order to apply Step 2A, a recitation of claims is copied below. The limitations of those claims which describe an abstract idea are bolded.
As per claim 10, the claim recites the limitations of:
A computer-implemented numerical simulation method for predicting a motion of a fluid governed by at least one differential equation (As drafted and under its broadest reasonable interpretation, this limitation amounts to an Abstract Idea (Mental Processes MPEP 2106.04(a)(2)(III)). Mental Processes are defined as concepts that can practically be performed in the human mind, or by a human using pen and paper as a physical aid. Examples of mental processes include observations, evaluations, judgments, and opinions. This limitation is directed towards performing a mental process on a generic computer, since a person can reasonably “predict” a motion of a fluid governed by a differential equation by solving that differential equation, with or without the aid of pen and paper. Additionally, the claim is directed towards Mathematical Concepts (e.g. differential equation) per MPEP 2106.04(a)(2)(I)). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations.), comprising:
predicting a global solution to said at least one differential equation in the simulation domain, (As drafted and under its broadest reasonable interpretation, this limitation amounts to an Abstract Idea (Mental Processes MPEP 2106.04(a)(2)(III)). This limitation is directed towards performing a mental process on a generic computer, since a person can reasonably “predict” a global solution to a differential equation, with or without the aid of pen and paper. Additionally, the claim is directed towards Mathematical Concepts (e.g. differential equation) per MPEP 2106.04(a)(2)(I))) by performing a computation step comprising:
(i) dividing the simulation domain into a set of pieces, wherein each piece of the set of pieces: (A) comprises an area within the simulation domain; and (B) shares an overlap area with each piece of the set of pieces that is horizontally, vertically, or diagonally adjacent to that piece, to allow local boundary conditions to be updated; (As drafted and under its broadest reasonable interpretation, this limitation amounts to an Abstract Idea (Mental Processes MPEP 2106.04(a)(2)(III)). This limitation is directed towards performing a mental process on a generic computer, since a person can reasonably divide, or segment into smaller overlapping pieces, a simulation domain (i.e. computation area), with or without the aid of pen and paper. Additionally, the claim is directed towards Mathematical Concepts per MPEP 2106.04(a)(2)(I). The act of performing a computation step, such as dividing the simulation domain into pieces (i.e. mathematical relationships), is interpreted as mathematical concepts. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.)
(ii) iterating through the set of pieces in a sequence, and for each piece of
the set of pieces: (A) cutting that piece from the simulation domain to create a local domain; predicting a local solution for that local domain; and (C) based on the local solution, updating the local boundary conditions for each piece of the set of pieces that is adjacent to that piece; (As drafted and under its broadest reasonable interpretation, this limitation amounts to an Abstract Idea (Mental Processes MPEP 2106.04(a)(2)(III)). This limitation is directed towards performing a mental process on a generic computer, since a person can reasonably divide (in sequential order) smaller pieces of the simulation domain (i.e. computation area) to create a local domain (i.e. smaller computation area), then predict (i.e. solve at least one differential equation) a local solution, and then update adjacent local boundary conditions, with or without the aid of pen and paper. Additionally, the claim is directed towards Mathematical Concepts per MPEP 2106.04(a)(2)(I)). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. The acts of performing computation steps, such as dividing the simulation domain into pieces (i.e. mathematical relationships), predicting a local solution (i.e. mathematical calculations), and updating local boundary conditions (i.e. mathematical relationships) are interpreted as mathematical concepts. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols. A claim that recites a mathematical calculation, when the claim is given its broadest reasonable interpretation in light of the specification, will be considered as falling within the "mathematical concepts" grouping. A mathematical calculation is a mathematical operation (such as multiplication) or an act of calculating using mathematical methods to determine a variable or number.)
(iii) determining a global solution by reconstructing the plurality of local
solutions associated with set of pieces; (As drafted and under its broadest reasonable interpretation, this limitation amounts to an Abstract Idea (Mental Processes MPEP 2106.04(a)(2)(III)). This limitation is directed towards performing a mental process on a generic computer, since a person can reasonably determine (i.e. solve at least one differential equation) a global solution by reconstructing the plurality of local solutions, with or without the aid of pen and paper. Additionally, the claim is directed towards Mathematical Concepts per MPEP 2106.04(a)(2)(I)).
Step 2A, Prong 2:
As per claim 10, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present Mere Instructions To Apply An Exception. In particular, the claim recites the additional limitations:
(a) launching a simulation, making it possible to define a simulation domain, and computation, (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Specifically, this limitation is directed towards mere instructions to implement an abstract idea or other exception on a computer. )
(b) using a machine learning algorithm, (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Per MPEP 2106.05(f)(2), this limitation “invokes computers or other machinery merely as a tool to perform an existing process (i.e. solving equations). Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more.” Specifically, requiring the use of a machine learning algorithm to tailor information (i.e. predict a global solution) and provide it to a user on a generic computer is interpreted as Mere Instructions to Apply an Exception.)
(B) using the machine learning algorithm, (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Per MPEP 2106.05(f)(2), this limitation “invokes computers or other machinery merely as a tool to perform an existing process (i.e. solving equations). Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more.” Specifically, requiring the use of a machine learning algorithm to tailor information (i.e. predict a global solution) and provide it to a user on a generic computer is interpreted as Mere Instructions to Apply an Exception.)
wherein the sequence for iterating through the set of pieces is configured to ensure that each piece after the first piece of the sequence has a shared overlap area with a preceding piece of the sequence (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Per MPEP 2106.05(f)(1), this limitation recites only the idea of a solution or outcome i.e. fails to recite details how the sequence is configured to ensure [...].)
Accordingly, these additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea when considered as an ordered combination and as a whole. Per MPEP 2106.05(f), “implementing an abstract idea on a generic computer, does not integrate the abstract idea into a practical application in Step 2A Prong Two [ ] similar to how the recitation of the computer in the claim in Alice amounted to mere instructions to apply the abstract idea of intermediated settlement on a generic computer.”
Step 2B:
For step 2B of the analysis, the Examiner must consider whether each claim limitation individually or as an ordered combination amounts to significantly more than the abstract idea. This analysis includes determining whether an inventive concept is furnished by an element or a combination of elements that are beyond the judicial exception. For limitations that were categorized as “apply it” or generally linking the use of the abstract idea to a particular technological environment or field of use, the analysis is the same.
The additional elements as described in Step 2A Prong 2 are not sufficient to amount to significantly more than the judicial exception because the additional limitations are considered directed towards mere instructions to apply an exception (referencing MPEP 2106.05(d)) per MPEP 2106.05(g).
Per MPEP 2106.05(d)(II), the courts have recognized the following relevant computer functions as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity: i. Receiving or transmitting data over a network, ii. Performing repetitive calculations, iii. Electronic recordkeeping, iv. Storing and retrieving information in memory.
For the foregoing reasons, claim 10 is directed to an abstract idea without significantly more and is rejected as not patent eligible under 35 U.S.C. 101.
Claim 11, further recites, wherein the machine learning model is a physics-informed local deep learning network trained by means of existing numerical simulations. The additional limitation further elaborates the machine learning model; therefore, the limitation is considered to further recite mere instructions to implement an abstract idea or other exception on a generic computer (Mere Instructions to Apply an Exception) – MPEP 2106.05(f). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 12, further recites, wherein the local boundary conditions are extracted by the machine learning model from existing numerical simulations cut into samples, each sample being associated with the local boundary conditions so as to form learning data. The additional limitations further recite mere instructions to implement an abstract idea or other exception on a generic computer (Mere Instructions to Apply an Exception) – MPEP 2106.05(f). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 13 has been canceled.
Claim 14, further recites, wherein the sequence is configured to iterate through the set of pieces left to right across a row of pieces of the simulation domain, and then from top to bottom of the simulation domain as the end of each row is reached. The additional limitations further recite mere instructions to implement an abstract idea or other exception on a generic computer (Mere Instructions to Apply an Exception) – MPEP 2106.05(f). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 15, further recites, wherein the computation step is iterative, the iteration being conditioned by a convergence of the global solution. The additional limitations further recite mere instructions to implement an abstract idea or other exception on a generic computer (Mere Instructions to Apply an Exception) – MPEP 2106.05(f). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 16, further recites, wherein said at least one differential equation is used to define a loss function. The additional limitation further recites Mathematical Concepts (MPEP 2106.04(a)(2)(I)) and/or mere instructions to implement an abstract idea or other exception on a generic computer (Mere Instructions to Apply an Exception, MPEP 2106.05(f)). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 17, further recites, wherein said at least one differential equation is a partial differential equation. The additional limitation further recites Mathematical Concepts (MPEP 2106.04(a)(2)(I)). Therefore, the claim is not patent eligible under 35 U.S.C. 101.
Claim 18, further recites, A computer program comprising a set of program code instructions executable by a processor to implement the numerical simulation method of claim 10. The additional limitation amounts to no more than mere instructions to implement an abstract idea or other exception on a computer (Mere Instructions to Apply an Exception) – MPEP 2106.05(f). For instance, the program itself merely implements (i.e. instructs) the abstract idea on a computer. Therefore, the claim is considered ineligible under 35 U.S.C. 101.
Claim 19 (new) further recites wherein the sequence for iterating through the set of pieces is further configured based upon at least one subject matter characteristics of the simulation. The additional element elaborates on the sequence for iterating, thus further amounts to Mental Processes and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I)/(III). Therefore, the claim is considered ineligible under 35 U.S.C. 101.
Claim 20 (new), the numerical simulation method of claim 19, further recites wherein the at least one subject matter characteristic of the simulation comprises the relative movement of an air flow around a profile, and wherein the sequence for iterating through the set of pieces is further configured to match the relative movement of the air flow around the profile. The additional element elaborates on the subject matter characteristics and sequence for iterating, thus further amounts to Mental Processes and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I)/(III). Therefore, the claim is considered ineligible under 35 U.S.C. 101.
Claim 21 (new) recites wherein the overlap area shared by pieces that are horizontally or vertically adjacent comprises an area of about 50% of each piece, and wherein the overlap area shared by pieces that are diagonally adjacent comprises an area of about 25% of each piece. The additional element elaborates on the divided simulation domain pieces, thus further amounts to Mental Processes and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I)/(III). Therefore, the claim is considered ineligible under 35 U.S.C. 101.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries set forth in Graham V. John Deere Co., 383 U.S. 1, 148 USPQ 459 (1966), that are applied for establishing a background for determining obviousness under 35 U.S.C. 103(a) are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or
nonobviousness.
Claims 10-12, 14-19, and 21 are rejected under 35 U.S.C. 103 as being unpatentable over Li, Ke, Kejun Tang, Tianfan Wu, and Qifeng Liao. "D3M: A deep domain decomposition method for partial differential equations." Ieee Access 8 (2019): 5283-5294. (hereinafter referred to as “Li”) in view of Sun, Luning, Han Gao, Shaowu Pan, and Jian-Xun Wang. "Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data." Computer Methods in Applied Mechanics and Engineering 361 (2019): 112732. (hereinafter referred to as “Sun”).
Regarding Claim 10, Li discloses,
(a) launching a simulation, making it possible to define a simulation domain, and computation (“the full procedure of D3M comprises the following steps:
pre-step: Set the architecture of neural networks in each subdomain;
offline step: Construct functions for boundary conditions, train networks and generate local solutions;
online step: Estimate target input data using neural networks. If solutions don't converge, transfer information on interfaces and go back to the offline step.” Li [Pg.5289 V.]. These steps are interpreted as “launching a simulation”.),
(b) using a machine learning algorithm, predicting a global solution to said at least one differential equation in the simulation domain, (“The local solution of PDEs on each subdomain is replaced by neural networks (i.e. machine learning algorithm) which can be trained through the variational principle, where the global solution on the whole domain consists of these local solutions on subdomains” Li [Pg.5286 Col.2 last paragraph]. The neural network is interpreted to include at least one differential equation because “The solution of PDEs can be formulated as the solution
of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem” Li [Pg.5283 Abstract])
by performing a computation step comprising:
(i) dividing the simulation domain into a set of pieces, wherein each
piece of the set of pieces: (A) comprises an area within the simulation domain; and (B) shares an overlap area with each piece of the set of pieces that is horizontally, vertically, or diagonally adjacent to that piece, to allow local boundary conditions to be updated; (“We first divide the domain Ω into
d
subdomains, and each two neighboring subdomains are overlapping.” Li [Pg.5286 Col.2 P.2]. See Figure 5 [Pg.5290] below for domain decomposition setting.)
PNG
media_image1.png
403
479
media_image1.png
Greyscale
(ii) iterating through the set of pieces in a sequence, and for each piece of
the set of pieces: (A) cutting that piece from the simulation domain to create a local domain; (B) using the machine learning algorithm, predicting a local solution for that local domain; (“The procedure of D3M is as follows. We first divide (i.e. cutting a piece) the domain Ω into d subdomains, and each two neighboring subdomains are overlapping. The local solution of PDEs on each subdomain is replaced by neural networks which can be trained (i.e. predicting a local solution) through the variational principle (i.e. includes boundary conditions), where the global solution on the whole domain consists of these local solutions on subdomains. To be more precise, let
Γ
i
denote decomposed junctions,
θ
is initial weights of neural networks,
η
is the threshold of accuracy,
S
i
and
g
i
are the samples generated in
Ω
i
and on interface
Γ
i
to evaluate the output of networks in each iteration” Li [Pg.5286 Col.2 P.2]) and (C) based on the local solution, updating the local boundary conditions for each piece of the set of pieces that is adjacent to that piece; (“We first divide (i.e. cut) the domain Ω (i.e. simulation domain) into d subdomains (i.e. cut pieces), and each two neighboring subdomains are overlapping” Li [Pg.5286 Col.2 P.2]. The local boundary conditions are interpreted to update because “the full procedure of D3M comprises the following steps:
pre-step: Set the architecture of neural networks in each subdomain;
offline step: Construct functions for boundary conditions, train networks and generate local solutions;
online step: Estimate target input data using neural networks. If solutions don't converge, transfer information on interfaces and go back to the offline step.” Li [Pg.5289 V.])
(iii) determining a global solution by reconstructing the plurality of local
solutions associated with set of pieces; (“The local solution of PDEs on
each subdomain is replaced by neural networks which can be trained through the variational principle, where the global solution on the whole domain consists of these local solutions on subdomains.” Li [Pg.5286 Col.2 P.2])
wherein the sequence for iterating through the set of pieces is configured
to ensure that each piece after the first piece of the sequence has a shared overlap area with a preceding piece of the sequence. (“In each subdomain, the convergence can be obtained from the Theorems 7.1 and 7.3 in [21]. With the Proposition 2, the sequence
{
N
i
n
}
η
∈
N
is uniform bounded in
n
, and the rates of convergence to the solution
u
* are related to overlapping areas.” Li [Pg.5289 Col.2 P.1])
Li fails to specifically disclose A computer-implemented numerical simulation method for predicting a motion of a fluid governed by at least one differential equation.
However, Sun discloses A computer-implemented numerical simulation method for predicting a motion of a fluid governed by at least one differential equation (“a deep neural network (DNN) architecture is built to approximate the solutions of the Navier–Stokes equations (i.e. differential equations) in a parametric setting. The DNN-based surrogate is expected to provide a rapid online prediction of the flow field with any given set of parameters” Sun [Pg.4 last paragraph])
Li and Sun are analogous art as they both relate to solving differential equations utilizing neural networks. Li teaches a deep domain decomposition method (D3M) based on the variational principle for PDEs. Li discloses, “The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems.” [Abstract]. And Sun teaches a physics-constrained deep learning approach for surrogate modeling of fluid flows. Sun discloses, “a structured deep neural network (DNN) architecture is devised to enforce the initial and boundary conditions, and the governing partial differential equations (i.e., Navier–Stokes equations) are incorporated into the loss of the DNN to drive the training” [Abstract]. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the computational efficiency of Li with the physics-informed neural networks of Sun in order to solve large-scale PDE based systems, such as fluid dynamics.
Claim 11, Li in view of Sun disclose the method of claim 10, Li further discloses, wherein the machine learning model is a local deep learning network trained by means of existing numerical simulations (“The development of using domain decomposition leads to an independent model-training procedure in each subdomain in an “offline” phase, followed by assembling global solution using pre-computed (i.e. existing numerical simulations) local information in an “online” phase” Li [Pg.5284 Col.1 C.])
Li fails to specifically disclose a physics-informed local deep learning network.
However, Sun discloses a physics-informed (“Therefore, penalizing the PDE residuals can regularize the data-driven DNN solutions to be more physical. This idea is known as the physics-informed, weakly-supervised deep learning” Sun [Pg.6 P.2.3]) local deep learning network.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the machine learning model of Li with the physics-informed neural networks of Sun in order “to assimilate multi-fidelity training data” Sun [Pg.3 Ln.6].
Claim 12, Li in view of Sun disclose the method of claim 10, Li further discloses, wherein the local boundary conditions are extracted by the machine learning model from existing numerical simulations cut into samples, (“The development of using domain decomposition leads to an independent model-training procedure in each subdomain (i.e. cut samples) in an “offline” phase, followed by assembling global solution using pre-computed (i.e. existing numerical simulations) local information (i.e. local boundary conditions) in an “online” phase” Li [Pg.5284 Col.1 C.]),
each sample being associated with the local boundary conditions so as to form learning data. (“To this end, we choose a mini-batch of points randomly sampled in Ω. These data points can give an estimation of the integral in (9) (i.e. includes local boundary conditions) and the gradient information to update the parameters Θ. For example, a mini-batch points {(xi; yi)}m+ni=1 are drawn in
Ω
(i.e. local domain) randomly, where {(xi; yi)}mi=1 in Ω and {(xi; yi)}m+ni=m+1 on
∂
Ω
” Li [Pg.5285 Col.1 last paragraph]).
Claim 13 has been canceled.
Claim 14, Li in view of Sun disclose the method of claim 10, Li further discloses, wherein the sequence is configured to iterate through the set of pieces left to right across a row of pieces of the simulation domain, and then from top to bottom of the simulation domain as the end of each row is reached. (“The domain decomposition setting is illustrated in Figure 5 (see below)” Li [Pg.5290 A.]. As can be seen in Figure 5 below, the sequence iterates from left to right (as evident by boundary conditions Ω1
∩
Ω2) and then from top to bottom (as evident by boundary conditions Ω1
∩
Ω3) of the simulation domain
∂
Ω1.)
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479
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Claim 15, Li in view of Sun disclose the method of claim 10, Li further discloses, wherein the computation step is iterative, the iteration being conditioned by a convergence of the global solution. (“D3M is developed based on iterative domain decomposition methods. The development of using domain decomposition leads to an independent model-training procedure in each subdomain in an “offline” phase, followed by assembling global solution using pre-computed local information in an “online'' phase” Li [Pg.5284 C.]. The iterative domain decomposition method is interpreted to being conditioned by a convergence of a global solution because “If solutions don't converge, transfer information on interfaces and go back to the offline step” Li [Pg.5289 V.])
Claim 16, Li in view of Sun disclose the method of claim 10, although Li fails to specifically disclose wherein said at least one differential equation is used to define a loss function.
However, Sun discloses, wherein said at least one differential equation is used to define a loss function. (“we consider leveraging the governing PDEs (i.e. partial differential equations) in the loss function” Sun [Pg.6 P.5]).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the computational efficiency of Li with the utilization of PDEs in the loss function, as Sun discloses, for “an accurate and efficient way to calculate derivatives” Sun [Pg.6 Ln.3].
Claim 17, Li in view of Sun disclose the method of claim 10, although Li fails to specifically disclose wherein said at least one differential equation is a partial differential equation.
However, Sun discloses, wherein said at least one differential equation is a partial differential equation. (“we consider leveraging the governing PDEs (i.e. partial differential equations) in the loss function” Sun [Pg.6 P.5]).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the computational efficiency of Li with the utilization of PDEs in the loss function, as Sun discloses, for “an accurate and efficient way to calculate derivatives” Sun [Pg.6 Ln.3].
Claim 18, Li in view of Sun disclose the method of claim 10, Li further discloses, A computer program comprising a set of program code instructions executable by a processor to implement the numerical simulation method of claim 10. (“our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems.” Li [Pg.5283 Abstract]. It is understood by one of ordinary skill in the art that neural networks consist of program code executed by a processor.
Claim 19 (new), Li in view of Sun disclose the method of claim 10, Li further discloses wherein the sequence for iterating through the set of pieces is further configured based upon at least one subject matter characteristics of the simulation. (The sequence for iterating disclosed by Li is interpreted to be configured based upon at least one subject matter characteristic due to the following disclosure, “When considering computational problems arising in practical engineering, e.g. aeronautics and astronautics (e.g. subject matter characteristics), systems are typically designed by multiple groups along disciplinary. The complexity of solving large-scale problems may take an expensive cost of hardware. The balance of accuracy and generalization is also hard to trade off. For this reason, decomposing a given system into component parts to manage the complexity is a strategy, and the domain decomposition method is a traditional numerical method to achieve this goal. [ ] In this work, we propose a variational deep learning solver based on domain decomposition methods, which is referred to as the deep domain decomposition method (D3M) to implement parallel computations along physical subdomains.” Li [Pg.5283 – 5284 P.1-2])
Claim 21 (new), Li in view of Sun disclose the method of claim 10, Li further discloses wherein the overlap area shared by pieces that are horizontally or vertically adjacent comprises an area of about 50% of each piece, and wherein the overlap area shared by pieces that are diagonally adjacent comprises an area of about 25% of each piece. (“
-
∆
u
(
x
,
y
)
=
1
,
i
n
Ω
u
(
x
,
y
)
=
0
,
o
n
∂
Ω
(36) where the physical domain is Ω = (-1,1) x (-1,1). The domain decomposition setting is illustrated in Figure 5 (see below).” Li [Pg.5290 Col.1 Sec. A])
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Claim 20 is rejected under 35 U.S.C. 103 as being unpatentable over Li, Ke, Kejun Tang, Tianfan Wu, and Qifeng Liao. "D3M: A deep domain decomposition method for partial differential equations." Ieee Access 8 (2019): 5283-5294. (hereinafter referred to as “Li”), in view of Sun, Luning, Han Gao, Shaowu Pan, and Jian-Xun Wang. "Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data." Computer Methods in Applied Mechanics and Engineering 361 (2019): 112732. (hereinafter referred to as “Sun”), in view of Bhatnagar, Saakaar, et al. "Prediction of aerodynamic flow fields using convolutional neural networks." Computational Mechanics 64.2 (2019): 525-545 (hereinafter referred to as “Bhatnagar”).
Claim 20 (new), Li in view of Sun disclose the method of claim 19, but fail to specifically disclose wherein the at least one subject matter characteristic of the simulation comprises the relative movement of an air flow around a profile, and wherein the sequence for iterating through the set of pieces is further configured to match the relative movement of the air flow around the profile.
However Bhatnagar discloses wherein the at least one subject matter characteristic of the simulation comprises the relative movement of an air flow around a profile, (“In this work, flow computations and analyses are performed using the OVERTURNS CFD code [ ] This code solves the compressible RANS equations [ ] Iterative solutions are pursued using the implicit approximate factorization method [ ] Simulations are performed over [ ] airfoils [ ] which contain a region of pressure recovery along the upper surface which induces a smooth transition from laminar to turbulent flow (so-called “transition-ramp").” Bhatnagar [Pg.3 Sec.2.1])
and wherein the sequence for iterating through the set of pieces is further configured to match the relative movement of the air flow around the profile. (“The network learns different weights during the training phase to predict the flow fields (i.e. air flow around the profile/airfoil). In each iteration, a batch of data undergoes the feed-forward process followed by a back-propagation” Bhatnagar [Pg.8 Sec.2.8])
Bhatnagar is analogous art as it relates to the prediction of aerodynamic flow fields using machine learning. Bhatnagar discloses an “approximation model based on convolutional neural networks (CNNs) is proposed for flow field predictions. The CNN is used to predict the velocity and pressure field in unseen flow conditions and geometries given the pixelated shape of the object” [Abstract]. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have modified the Li-Sun combination to include simulation subject matter comprising the relative movement of air flow around a profile in order “to extract relevant features from fluid dynamics data and to predict the entire flow field in near real-time.” Bhatnagar [Pg.4 Sec. 2.2].
Conclusion
The prior art made of record, listed on form PTO-892, and not relied upon is
considered pertinent to applicant's disclosure:
Kjolstad, Fredrik Berg, and Marc Snir. "Ghost cell pattern." Proceedings of the 2010 Workshop on Parallel Programming Patterns. 2010. “Many problems can be modeled as a set of points in a structured grid that are updated in successive iterations based on the values of their neighbors from the previous iteration. These problems can be divided geometrically into chunks that are computed on different processors or cores.” [Pg.1 Sec.1]
Grinberg, Leopold, and George E. Karniadakis. "A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows." Journal of Computational Physics 229.15 (2010): 5541-5563. “a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources.” [Abstract]
Belbute-Peres, Filipe De Avila, Thomas Economon, and Zico Kolter. "Combining differentiable PDE solvers and graph neural networks for fluid flow prediction." international conference on machine learning. PMLR, 2020. “Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process.” [Abstract]
Applicant’s amendment necessitated the new ground(s) of rejection presented in this Office Action. Accordingly, THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Anthony Chavez whose telephone number is (571) 272-1036. The examiner can normally be reached Monday - Thursday, 8 a.m. - 5 p.m. ET.
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/ANTHONY CHAVEZ/ Examiner, Art Unit 2187
/RENEE D CHAVEZ/ Supervisory Patent Examiner, Art Unit 2186
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