Equation Discovery

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Most implemented papers archive 2025-07-28

30 shown of 34 papers with code (65 tagged with this task in all), ordered by repositories listed in the archive, not by stars (the archive holds no stars, so PwC's “Social” and “Latest” sorts cannot be reproduced). Papers without a page here are shown as plain text.

• Automated Mathematical Equation Structure Discovery for Visual Analysis
  17 Apr 2021 3 repositories listed
  In this paper, we focus on recent AI advances to present a novel framework for automatically discovering equations from scratch with little human intervention to deal with the different challenges encountered in…
• LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models
  14 Apr 2025 2 repositories listed Syntology ran 4 of 4 samples · 0 unverified
  Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena.
• LLM-SR: Scientific Equation Discovery via Programming with Large Language Models
  29 Apr 2024 2 repositories listed
  Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines.
• SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training
  3 Oct 2023 2 repositories listed Syntology ran 5 of 5 samples · 0 unverified · 1 pointer-only (licence)
  To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training model, which employs contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the embeddings.
• Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challenges
  8 Jun 2023 2 repositories listed
  These closures depend on nonlinear combinations of gradients of filtered variables, with constants that are independent of the fluid/flow properties and only depend on filter type/size.
• PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning
  1 Nov 2021 2 repositories listed
  We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a principled sparse regression algorithm to identify the hidden dynamics that govern a system's response.
• Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case
  1 Oct 2021 2 repositories listed
  Models of many engineering and natural systems are imperfect.
• Neural-Guided Equation Discovery
  21 Mar 2025 1 repository listed
  The system uses neural-guided Monte-Carlo Tree Search (MCTS) and supports both supervised and reinforcement learning, with a search space defined by a context-free grammar.
• Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework
  5 Feb 2025 1 repository listed
  Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data.
• Knowledge-aware equation discovery with automated background knowledge extraction
  31 Dec 2024 1 repository listed
  In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations.
• Equation discovery framework EPDE: Towards a better equation discovery
  28 Dec 2024 1 repository listed
  In this paper, we enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework.
• Adaptation of uncertainty-penalized Bayesian information criterion for parametric partial differential equation discovery
  15 Aug 2024 1 repository listed
  Data-driven discovery of partial differential equations (PDEs) has emerged as a promising approach for deriving governing physics when domain knowledge about observed data is limited.
• Discovering symbolic expressions with parallelized tree search
  5 Jul 2024 1 repository listed Syntology ran 8 of 10 samples · 2 unverified
  Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data.
• Amortized Equation Discovery in Hybrid Dynamical Systems
  6 Jun 2024 1 repository listed
  Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states.
• Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data
  30 May 2024 1 repository listed
  Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations…
• Symmetry-Informed Governing Equation Discovery
  27 May 2024 1 repository listed
  Depending on the types of symmetries, we develop a pipeline for incorporating symmetry constraints into various equation discovery algorithms, including sparse regression and genetic programming.
• LLM4ED: Large Language Models for Automatic Equation Discovery
  13 May 2024 1 repository listed
  The first strategy is to take LLMs as a black-box optimizer and achieve equation self-improvement based on historical samples and their performance.
• Mechanistic Neural Networks for Scientific Machine Learning
  20 Feb 2024 1 repository listed Syntology ran 1 of 1 samples · 0 unverified · 1 pointer-only (licence)
  This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences.
• GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations
  18 Dec 2023 1 repository listed
  In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent…
• Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots
  28 Nov 2023 1 repository listed
  Type 1: Approximate an unknown function given input/output data.
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
  9 Oct 2023 1 repository listed
  To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra to enable efficient computation and…
• Latent Space Symmetry Discovery
  29 Sep 2023 1 repository listed Syntology ran 14 of 18 samples · 4 unverified · 18 pointer-only (licence)
  Theoretically, we show that our model can express nonlinear symmetries under some conditions about the group action.
• Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert
  18 Aug 2023 1 repository listed
  The optimization techniques leveraged in this paper allow our approach to run in polynomial time with fully correct background theory under an assumption that the complexity of our derivation is bounded), or…
• Towards true discovery of the differential equations
  9 Aug 2023 1 repository listed
  Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications.
• Directed differential equation discovery using modified mutation and cross-over operators
  9 Aug 2023 1 repository listed
  The discovery of equations with knowledge of the process origin is a tempting prospect.
• Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation Discovery
  29 Jun 2023 1 repository listed
  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…
• Transformer-based Planning for Symbolic Regression
  13 Mar 2023 1 repository listed Syntology ran 4 of 8 samples · 4 unverified
  Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation…
• Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty
  14 Oct 2022 1 repository listed
  The equation residuals are used to inform the spline learning in a Bayesian manner, where approximate Bayesian uncertainty calibration techniques are employed to approximate posterior distributions of the trainable…
• Discovering stochastic dynamical equations from biological time series data
  5 May 2022 1 repository listed
  However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the role of stochasticity in real datasets.
• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
  29 Apr 2022 1 repository listed
  Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for second order IPSs to model the movement of communities of cells.

Syntology lines on 6 of the papers shown; no Syntology record for the others (a paper without an arXiv id cannot be joined to the graph, and absence from the graph layer is not a recorded non-run). “Ran” means the sample executed on a synthesized fixture, not that the paper's result was reproduced. Read from the graph 2026-09-24.