DATA-DRIVEN METHOD FOR DISCOVERING CONSERVATION PRINCIPLES IN PHYSICAL SYSTEMS

DETAILED ACTION Claims 1 – 20, which are currently pending, are fully considered below. Claims 1 and 14 are amended. No claims are added. No claims are canceled. 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 . Response to Arguments Applicant's arguments filed July 29, 2026 have been fully considered but they are not persuasive. Applicant argues, “Without waiver or disclaimer, and solely in an effort to further prosecution, claim 1 has been amended to recite, in combination with the other limitations of the claim, "evaluating collected data by a representation learning system, wherein the representation learning system is applied in a training physical system to extract information about the training physical system, and the evaluating collected data uses the extracted information in an at-issue physical system to make a prediction about the collected data." The human mind cannot practically be applied in a training physical system to extract information about the training physical system and subsequently be applied in an at-issue system to make a prediction using the extracted information, (Remarks, page 9). Examiner appreciates applicant’s attempt to amend the claims, but respectfully disagrees. The instant claim limitation reads, “A method for uncovering a conservation law in physical systems, the method comprising: evaluating collected data by a representation learning system, wherein the representation learning system is applied in a training physical system to extract information about the training physical system, and the evaluating collected data uses the extracted information in an at issue physical system to make a prediction about collected data. The human mind can most certainly evaluate data. Merely adding a physical system does not overcome 101. MENTAL PROCESSES MPEP 2106.04(a)(2)(III). The courts consider a mental process (thinking) that "can be performed in the human mind, or by a human using a pen and paper" to be an abstract idea. CyberSource Corp. v. Retail Decisions, Inc., 654 F.3d 1366, 1372, 99 USPQ2d 1690, 1695 (Fed. Cir. 2011). As the Federal Circuit explained, "methods which can be performed mentally, or which are the equivalent of human mental work, are unpatentable abstract ideas the ‘basic tools of scientific and technological work’ that are open to all.’" 654 F.3d at 1371, 99 USPQ2d at 1694 (citing Gottschalk v. Benson, 409 U.S. 63, 175 USPQ 673 (1972)). See also Mayo Collaborative Servs. v. Prometheus Labs. Inc., 566 U.S. 66, 71, 101 USPQ2d 1961, 1965 (2012) ("‘[M]ental processes[] and abstract intellectual concepts are not patentable, as they are the basic tools of scientific and technological work’" (quoting Benson, 409 U.S. at 67, 175 USPQ at 675)); Parker v. Flook, 437 U.S. 584, 589, 198 USPQ 193, 197 (1978) (same). Accordingly, the "mental processes" abstract idea grouping is defined as concepts performed in the human mind, and examples of mental processes include observations, evaluations, judgments, and opinions. The courts do not distinguish between mental processes that are performed entirely in the human mind and mental processes that require a human to use a physical aid (e.g., pen and paper or a slide rule) to perform the claim limitation. See, e.g., Benson, 409 U.S. at 67, 65, 175 USPQ at 674-75, 674 (noting that the claimed "conversion of [binary-coded decimal] numerals to pure binary numerals can be done mentally," i.e., "as a person would do it by head and hand."); Synopsys, Inc. v. Mentor Graphics Corp., 839 F.3d 1138, 1139, 120 USPQ2d 1473, 1474 (Fed. Cir. 2016) (holding that claims to a mental process of "translating a functional description of a logic circuit into a hardware component description of the logic circuit" are directed to an abstract idea, because the claims "read on an individual performing the claimed steps mentally or with pencil and paper"). Nor do the courts distinguish between claims that recite mental processes performed by humans and claims that recite mental processes performed on a computer. As the Federal Circuit has explained, "[c]ourts have examined claims that required the use of a computer and still found that the underlying, patent-ineligible invention could be performed via pen and paper or in a person’s mind." Versata Dev. Group v. SAP Am., Inc., 793 F.3d 1306, 1335, 115 USPQ2d 1681, 1702 (Fed. Cir. 2015). See also Intellectual Ventures I LLC v. Symantec Corp., 838 F.3d 1307, 1318, 120 USPQ2d 1353, 1360 (Fed. Cir. 2016) (‘‘[W]ith the exception of generic computer-implemented steps, there is nothing in the claims themselves that foreclose them from being performed by a human, mentally or with pen and paper.’’); Mortgage Grader, Inc. v. First Choice Loan Servs. Inc., 811 F.3d 1314, 1324, 117 USPQ2d 1693, 1699 (Fed. Cir. 2016) (holding that computer-implemented method for "anonymous loan shopping" was an abstract idea because it could be "performed by humans without a computer"). Because both product and process claims may recite a "mental process", the phrase "mental processes" should be understood as referring to the type of abstract idea, and not to the statutory category of the claim. The courts have identified numerous product claims as reciting mental process-type abstract ideas, for instance the product claims to computer systems and computer-readable media in Versata Dev. Group. v. SAP Am., Inc., 793 F.3d 1306, 115 USPQ2d 1681 (Fed. Cir. 2015). Applicant argues, without waiver or disclaimer, and solely in an effort to further prosecution, claim 1 has been further amended to recite, in combination with the other limitations of the claim, "analyzing the collected data by a topological learning analysis system, wherein the topological learning analysis system analyzes the collected data with an insensitivity to a previously chosen metric and reduces a dimensionality of the collected data, and transferring the collected data into at least two displayable trajectories, wherein the trajectories are each of a multi-dimensional form." The human mind cannot practically be applied as a separate topology learning analysis system with an insensitivity to a previously chosen metric and reduces a dimensionality of the collected data, such that the resulting displayable trajectories are each of a multi-dimensional form, (Remarks, page 9). Examiner respectfully disagrees, and notes that the human mind can perform analysis. Applicant argues, without waiver or disclaimer, and solely in an effort to further prosecution, claim 1 has been further amended to recite, in combination with the other limitations of the claim, generating a distance matrix by computing Wasserstein distances between the trajectories, with the distance matrix defining a structure of a shape space between the trajectories." The human mind cannot practically compute an exact Wasserstein distance matrix defining a structure of a shape space between trajectories, (Remarks, page 9). Examiner respectfully disagrees, and a human mind can perform computing, but this may also be viewed as a mathematical concept. MATHEMATICAL CONCEPTS The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. MPEP 2106.04(a)(2)(I). The Supreme Court has identified a number of concepts falling within this grouping as abstract ideas including: a procedure for converting binary-coded decimal numerals into pure binary form, Gottschalk v. Benson, 409 U.S. 63, 65, 175 USPQ2d 673, 674 (1972); a mathematical formula for calculating an alarm limit, Parker v. Flook, 437 U.S. 584, 588-89, 198 USPQ2d 193, 195 (1978); the Arrhenius equation, Diamond v. Diehr, 450 U.S. 175, 191, 209 USPQ 1, 15 (1981); and a mathematical formula for hedging, Bilski v. Kappos, 561 U.S. 593, 611, 95 USPQ 2d 1001, 1004 (2010). The Court’s rationale for identifying these "mathematical concepts" as judicial exceptions is that a ‘‘mathematical formula as such is not accorded the protection of our patent laws,’’ Diehr, 450 U.S. at 191, 209 USPQ at 15 (citing Benson, 409 U.S. 63, 175 USPQ 673), and thus ‘‘the discovery of [a mathematical formula] cannot support a patent unless there is some other inventive concept in its application.’’ Flook, 437 U.S. at 594, 198 USPQ at 199. In the past, the Supreme Court sometimes described mathematical concepts as laws of nature, and at other times described these concepts as judicial exceptions without specifying a particular type of exception. See, e.g., Benson, 409 U.S. at 65, 175 USPQ2d at 674; Flook, 437 U.S. at 589, 198 USPQ2d at 197; Mackay Radio & Telegraph Co. v. Radio Corp. of Am., 306 U.S. 86, 94, 40 USPQ 199, 202 (1939) (‘‘[A] scientific truth, or the mathematical expression of it, is not patentable invention[.]’’). More recent opinions of the Supreme Court, however, have affirmatively characterized mathematical relationships and formulas as abstract ideas. See, e.g., Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S. 208, 218, 110 USPQ2d 1976, 1981 (2014) (describing Flook as holding "that a mathematical formula for computing ‘alarm limits’ in a catalytic conversion process was also a patent-ineligible abstract idea."); Bilski v. Kappos, 561 U.S. 593, 611-12, 95 USPQ2d 1001, 1010 (2010) (noting that the claimed "concept of hedging, described in claim 1 and reduced to a mathematical formula in claim 4, is an unpatentable abstract idea,"). It is important to note that a mathematical concept need not be expressed in mathematical symbols, because "[w]ords used in a claim operating on data to solve a problem can serve the same purpose as a formula." In re Grams, 888 F.2d 835, 837 and n.1, 12 USPQ2d 1824, 1826 and n.1 (Fed. Cir. 1989). See, e.g., SAP America, Inc. v. InvestPic, LLC, 898 F.3d 1161, 1163, 127 USPQ2d 1597, 1599 (Fed. Cir. 2018) (holding that claims to a ‘‘series of mathematical calculations based on selected information’’ are directed to abstract ideas); Digitech Image Techs., LLC v. Elecs. for Imaging, Inc., 758 F.3d 1344, 1350, 111 USPQ2d 1717, 1721 (Fed. Cir. 2014) (holding that claims to a ‘‘process of organizing information through mathematical correlations’’ are directed to an abstract idea); and Bancorp Servs., LLC v. Sun Life Assurance Co. of Can. (U.S.), 687 F.3d 1266, 1280, 103 USPQ2d 1425, 1434 (Fed. Cir. 2012) (identifying the concept of ‘‘managing a stable value protected life insurance policy by performing calculations and manipulating the results’’ as an abstract idea). Accordingly, examiner maintains the rejection, and this Office Action is made Final. 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 1 - 20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of mental processes and/or math without significantly more. As to claim 1, the claim recites the mental processes of evaluating collected data by a representation learning system, by analyzing the collected data by a topological learning analysis system, and transferring the data into at least two displayable trajectories. (A person can mentally evaluate and analyze data). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Although the claim discloses generating a distance matrix by computing Wasserstein distances between the trajectories, with the distance matrix showing a shape space between the trajectories; embedding the shape space of the distance matrix into lower dimensions by using a uniform manifold approximation and projection (UMAP); and determining at least two scores for different embeddings to choose a score. The claim represents at least one of the shape space, or a minimal dimensionality and uses a symbolic regression to identify a closed form of integrals of motion. Nothing is actually done with the data besides determining a score, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 2, the claim recites the mental processes wherein the trajectory is represented by at least two points on the trajectory, wherein each point represents at least one data, respectively. (A person can mentally represent data on a trajectory). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 3, the claim recites the mental processes wherein the trajectory is ergodic and amplitudes of at least two variations in different conserved qualities have similar effect on the Wasserstein distance. (A person can mentally represent data on a trajectory). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 4, the claim recites the mental processes of normalizing the Wasserstein distances data, including by a zero mean and/or a unit maximal value. (A person can mentally represent data on a trajectory). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 5, the claim recites the mental processes of varying an output metric hyper parameter of the UMAP controls a topology of a target space. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 6, the claim recites the mental processes wherein the topology of the target space is controlled by using a distance on a circle along an arc. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 7, the claim recites the mental processes wherein the topological learning system defines a target space. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 8, the claim recites the mental processes wherein the UMAP comprises an output metric hyper parameter. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 9, the claim recites the mental processes wherein the target space is controlled by varying the output metric hyper parameter of the UMAP. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 10, the claim recites the mental processes wherein the representation of the shape space by the embedding is measured by a neighbor deviation score (NDS). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 11, the claim recites the mental processes wherein the NDS utilizes a reference trajectory. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 12, the claim recites the mental processes wherein the NDS is an average absolute deviation in rank of at least two points on the trajectory. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 13, the claim recites the mental processes of determining distances from all trajectories to the reference trajectory. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 14, the claim recites the mental processes of evaluating collected data by a representation learning system, by analyzing the collected data by a topological learning analysis system, and transferring the data into at least two displayable trajectories. (A person can mentally evaluate and analyze data). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Although the claim discloses generating a distance matrix by computing Wasserstein distances between the trajectories, with the distance matrix showing a shape space between the trajectories; embedding the shape space of the distance matrix into lower dimensions by using a uniform manifold approximation and projection (UMAP); and determining at least two scores for different embeddings to choose a score. The claim represents at least one of the shape space, or a minimal dimensionality and uses a symbolic regression to identify a closed form of integrals of motion. Nothing is actually done with the data besides determining a score, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 15, the claim recites the mental processes wherein the trajectory is represented by at least two points on the trajectory, wherein each point represents at least one data, respectively. (A person can mentally represent data on a trajectory). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 16, the claim recites the mental processes wherein the trajectory is ergodic and amplitudes of at least two variations in different conserved qualities have similar effect on the Wasserstein distance. (A person can mentally represent data on a trajectory). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 17, the claim recites the mental processes of normalizing the Wasserstein distances data, including by a zero mean and/or a unit maximal value. (A person can mentally represent data). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 18, the claim recites the mental processes of varying an output metric hyper parameter of the UMAP controls a topology of a target space. A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 19, the claim recites the mental processes wherein the representation of the shape space by the embedding is measured by a neighbor deviation score (NDS). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Nothing is actually done with the data, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As to claim 20, the claim recites the mental processes of analyzing the collected data by a topological learning analysis system, and transferring the data into at least two displayable trajectories. (A person can mentally evaluate and analyze data). A judicial exception is not integrated into a practical application because there are no steps beyond the abstract idea to possibly integrate it into a practical application. Although the claim discloses computing at least one distance and generating a matrix, nothing is actually done with the data besides determining a score, let alone any meaningful way that could amount to any practical application. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. Conclusion 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. Contact Information Any inquiry concerning this communication or earlier communications from the examiner should be directed to ALEXANDRIA Y BROMELL whose telephone number is (571)270-3034. The examiner can normally be reached M-F 8-4. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. 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If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /ALEXANDRIA Y BROMELL/Primary Examiner, Art Unit 2156 March 30, 2026