I1. the complete title of one (or more) paper(s) published in the open literature describing the work that the author claims describes a human-competitive result;

The series of the papers, including:

[1] Maslyaev, M., & Hvatov, A. (2023, June). The data-driven physical-based equations discovery using evolutionary approach. In Proceedings of the 2023 Genetic and Evolutionary Computation Conference Companion (In press, unconditionally accepted)
[2] Ivanchick, E., & Hvatov, A., (2023, June). Directed differential equation discovery using modified mutation and cross-over operators. In 2023 IEEE Congress on Evolutionary Computation (CEC). (In press, unconditionally accepted)
[3] Maslyaev, M., & Hvatov, A. (2023, January). Multiobjective evolutionary discovery of equation-based analytical models for dynamical systems. Journal Scientific and Technical Of Information Technologies, Mechanics and Optics, 147(1), 97.
[4] Maslyaev, M., & Hvatov, A. (2022, July). Solver-Based Fitness Function for the Data-Driven Evolutionary Discovery of Partial Differential Equations. In 2022 IEEE Congress on Evolutionary Computation (CEC) (pp. 1-8). IEEE.


2. the name, complete physical mailing address, e-mail address, and phone number of EACH author of EACH paper(s);

Alexander Hvatov

email: alex_hvatov@itmo.ru
phone: +7 952 220 32 76

ITMO University 
49 Kronverksky Pr. 
St. Petersburg
197101
Russian Federation


Mikhail Maslyaev
email: mikemaslyaev@itmo.ru
phone: +7 915 145 97 25

ITMO University 
49 Kronverksky Pr. 
St. Petersburg
197101
Russian Federation


Elizaveta Ivanchik

email: eaivanchik@itmo.ru
phone: +7 981 803 9522

ITMO University 
49 Kronverksky Pr. 
St. Petersburg
197101
Russian Federation




3. the name of the corresponding author (i.e., the author to whom notices will be sent concerning the competition);

AH

4. the abstract of the paper(s);

[1] Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizatioal problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.
[2] The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the evolutionary equation discovery, which allows modification of almost every optimization stage. In this paper, we examine the modifications that can be introduced into the evolutionary operators of the equation discovery algorithm, taking inspiration from directed evolution techniques employed in fields such as chemistry and biology. The resulting approach, dubbed directed equation discovery, demonstrates a greater ability to converge towards accurate solutions than the conventional method. To support our findings, we present experiments based on Burgers', wave, and Korteweg--de Vries equations.
[3] In this article, an approach to modeling dynamical systems in case of unknown governing physical laws has beenintroduced. The systems of differential equations obtained by means of a data-driven algorithm are taken as the desiredmodels. In this case, the problem of predicting the state of the process is solved by integrating the resulting differentialequations. In contrast to classical data-driven approaches to dynamical systems representation, based on the generalmachine learning methods, the proposed approach is based on the principles, comparable to the analytical equation-basedmodeling. Models in forms of systems of differential equations, composed as combinations of elementary functions andoperation with the structure, were determined by adapted multi-objective evolutionary optimization algorithm. Timeseries describing the state of each element of the dynamic system are used as input data for the algorithm. To ensurethe correct operation of the algorithm on data characterizing real-world processes, noise reduction mechanisms areintroduced in the algorithm. The use of multicriteria optimization, held in the space of complexity and quality criteriafor individual equations of the differential equation system, makes it possible to improve the diversity of proposedcandidate solutions and, therefore, to improve the convergence of the algorithm to a model that best represents thedynamics of the process. The output of the algorithm is a set of Pareto-optimal solutions of the optimization problemwhere each individual of the set corresponds to one system of differential equations. In the course of the work, a libraryof data-driven modeling of dynamic systems based on differential equation systems was created. The behavior of thealgorithm was studied on a synthetic validation dataset describing the state of the hunter-prey dynamic system given bythe Lotka-Volterra equations. Finally, a toolset based on the solution of the generated equations was integrated into thealgorithm for predicting future system states. The method is applicable to data-driven modeling of arbitrary dynamicalsystems (e.g. hydrometeorological systems) in cases where the processes can be described using differential equations.Models generated by the algorithm can be used as components of more complex composite models, or in an ensembleof methods as an interpretable component. 
[4] Partial differential equations provide accurate models for many physical processes, although their derivation can be challenging, requiring a fundamental understanding of the modeled system. This challenge can be circumvented with the data-driven algorithms that obtain the governing equation only using observational data. One of the tools commonly used in search of the differential equation is the evolutionary optimization algorithm. In this paper, we seek to improve the existing evolutionary approach to data-driven partial differential equation discovery by introducing a more reliable method of evaluating the quality of proposed structures, based on the inclusion of the automated algorithm of partial differential equations solving. In terms of evolutionary algorithms, we want to check whether the more computationally challenging fitness function represented by the equation solver gives the sufficient resulting solution quality increase with respect to the more simple one. The approach includes a computationally expensive equation solver compared with the baseline method, which utilized equation discrepancy to define the fitness function for a candidate structure in terms of algorithm convergence and required computational resources on the synthetic data obtained from the solution of the Korteweg-de Vries equation.

5. a list containing one or more of the eight letters (A, B, C, D, E, F, G, or H) that correspond to the criteria (see above) that the author claims that the work satisfies;

(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
(G) The result solves a problem of indisputable difficulty in its field.

6. a statement stating why the result satisfies the criteria that the contestant claims (see examples of statements of human-competitiveness as a guide to aid in constructing this part of the submission);

(B) Partial differential equations (PDE) discovery has gained significant momentum, with claims that any equation can be restored from data. While this assertion is not entirely accurate, recent advancements have improved equation restoration techniques. Traditionally, sparse regression on a large, predefined terms library has been used. However, a new approach, as demonstrated in [ES], involves sampling smaller sub-libraries to assess uncertainty. Most equation discovery algorithms are evaluated based on their ability to recover known equations. Typically, this involves numerically solving equations, introducing noise to the obtained data, and then adding terms to the large library to ultimately rediscover the initial equation.

Evolutionary algorithms offer a more natural approach to generate small libraries by employing random term changes through mutation operators and term exchanges through cross-over. This approach represents a significant step forward in the quest to discover unknown equations. The concept of multi-objectiveness [1,3] allows us to handle systems with independent equations more effectively and enhances the overall discovery of single equations. Incorporating an automated solver [AH] enables us to assess uncertainty by directly comparing solutions with the data. In contrast to the current state-of-the-art [ES], where the solver is set up to solve a specific equation and discovered equations are truncated to fit that form, our approach provides greater flexibility. We can explore all discovered equations and analyze the joint term co-appearance distribution along with the coefficient. Additionally, by incorporating modified cross-over and mutation operators [2], we introduce a directionality to the search process, akin to library cherry-picking, while still allowing for various forms of resulting equations.

In summary, evolutionary equation discovery surpasses the state-of-the-art [ES] in three key aspects: (1) uncovering unknown equations, (2) identifying equations from noisy data, and (3) assessing uncertainty through co-appearance analysis. A recent paper on algebraic models [IBM], distinct from differential equations, supports our approach by demonstrating the efficacy of a multi-objective methodology in obtaining broader models in the form of differential equation systems [MO]. We are pleased to share our findings and provide open-source code at https://github.com/ITMO-NSS-team/EPDE.

[ES] Fasel, U., Kutz, J. N., Brunton, B. W., & Brunton, S. L. (2022). Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control. Proceedings of the Royal Society A, 478(2260), 20210904.
[AH] Hvatov, A. (2023). Automated differential equation solver based on the parametric approximation optimization. Mathematics, 11(8), 1787.
[IBM] Cornelio, C., Dash, S., Austel, V., Josephson, T. R., Goncalves, J., Clarkson, K. L., ... & Horesh, L. (2023). Combining data and theory for derivable scientific discovery with AI-Descartes. Nature Communications, 14(1), 1777.
[MO] Maslyaev, M., & Hvatov, A. (2021, June). Multi-objective discovery of PDE systems using evolutionary approach. In 2021 IEEE Congress on Evolutionary Computation (CEC) (pp. 596-603). IEEE.


(G) It is hard to open an undiscovered law in the form of the differential equation in modern physics. However, we could try to extract one from data without any preliminary assumptions to see if the computer way of thinking (modus ponens) is agreed with the human one. We teach the computer to discover physics parallel to the human way. It should inspire the scientist to find the new laws and the new ways to make the physics.

7. a full citation of the paper (that is, author names; title, publication date; name of journal, conference, or book in which article appeared; name of editors, if applicable, of the journal or edited book; publisher name; publisher city; page numbers, if applicable);

[1] Maslyaev, M., & Hvatov, A. (2023, June). The data-driven physical-based equations discovery using evolutionary approach. In Proceedings of the 2023 Genetic and Evolutionary Computation Conference Companion (In press, unconditionally accepted)
[2] Ivanchick, E., & Hvatov, A., (2023, June). Directed differential equation discovery using modified mutation and cross-over operators. In 2023 IEEE Congress on Evolutionary Computation (CEC). (In press, unconditionally accepted)
[3] Maslyaev, M., & Hvatov, A. (2023, January). Multiobjective evolutionary discovery of equation-based analytical models for dynamical systems. Journal Scientific and Technical Of Information Technologies, Mechanics and Optics, 147(1), 97.
[4] Maslyaev, M., & Hvatov, A. (2022, July). Solver-Based Fitness Function for the Data-Driven Evolutionary Discovery of Partial Differential Equations. In 2022 IEEE Congress on Evolutionary Computation (CEC) (pp. 1-8). IEEE.

8. a statement either that "any prize money, if any, is to be divided equally among the co-authors" OR a specific percentage breakdown as to how the prize money, if any, is to be divided among the co-authors;

Any prize money, if any, is to be divided equally among all co-authors AH, MM, and EI.

9. a statement stating why the authors expect that their entry would be the "best"
Generative models are on fire. We create burning hot evolutionary differential equation dicovery algorithm that allows to uncover all nature secrets.

10. An indication of the general type of genetic or evolutionary computation used, such as GA (genetic algorithms), GP (genetic programming), ES (evolution strategies), EP (evolutionary programming), LCS (learning classifier systems), GI (genetic improvement), GE (grammatical evolution), GEP (gene expression programming), DE (differential evolution), etc.

GP

11. The date of publication of each paper. If the date of publication is not on or before the deadline for submission, but instead, the paper has been unconditionally accepted for publication and is "in press" by the deadline for this competition, the entry must include a copy of the documentation establishing that the paper meets the "in press" requirement.

[1] 2023, June
[2] 2023, June
[3] 2023, January
[4] 2022, July