ODE Discovery

ODE: Ordinary Differential Equation

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1 paper in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Latest papers 17

Oct 5, 2026q-bio.QM

APOD: reasoning-guided agentic population ordinary differential equation discovery for pharmacological digital twins

Establishing ordinary differential equations (ODEs) describing population data is a fundamental part of mathematical modeling in pharmacology, crucial to developing digital twins. However, doing so from sparse, noisy data is a slow, expert-driven task. Existing automated methods either search a restricted model space or ignore population inter-individual variability. Here we introduce APOD (Agentic Population ODE Discovery), a language-model agent that iteratively reasons over biological knowledge and fit diagnostics in an open-ended search space to discover a population digital twin (PDT), i.e., a shared ODE system with between-subject variability. On synthetic pharmacokinetic and tumor-dynamics benchmarks, APOD recovered ground-truth structures in 94-100% of runs, 12-fold faster in median than an established library-based search. On real cohorts it converged to valid structures, and proposed a PDT of radioligand-therapy-induced platelet dynamics that predicts thrombocytopenia from first-cycle data and simulates alternative dosing schedules that lower the predicted risk of toxicity.

Romain Ferrara, Martin Soucail, Victor Gertner +7

COMPutational pharmacology and clinical Oncology (COMPO), Inria Center at University Côte d’Azur, Cancer Research Center of Marseille, Marseille, France · Department of Nuclear Medicine, Institut Paoli-Calmettes, ENETS Center of Excellence, IPC NET Center, Marseille, France · Centre for Computational Biology (CBIO), Mines Paris, PSL University, Paris, France +3

Digital Twins Large Language Model-Guided Scientific Discovery ODE Discovery

Sep 29, 2026cs.LG

Identifying ODEs from Unstructured Data with Causal Representation Learning

We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing methods for ODE discovery typically assume direct measurements of the variables, or do not provide theoretical guarantees on the learned variables and equations. While Causal Representation Learning (CRL) methods provide guarantees on identifying variables from high-dimensional observations up to component-wise diffeomorphisms, we show that in general these variables cannot be used directly as input to equation discovery methods, which typically assume that the variables will lead to sparse equations. So we introduce SParse Equivalent Equation Discovery AutoEncoder (SPEED-AE), a framework that combines a pretrained CRL method with a component-wise autoencoder that learns transformations of variables that are amenable to sparse ODE discovery. We show that for polynomial ODEs, this additional step allows us to restrict the identifiability of each variable from polynomial to monomial diffeomorphisms. Experiments on Lotka-Volterra, Lorenz, and a two-pendulum system show that SPEED-AE improves on the disentanglement of the CRL methods and that it recovers ODEs that are closest to the ground truth, while achieving state-of-the-art forecasting performance.

Alessandro Trenta, Riccardo Massidda, Davide Bacciu +1

Department of Computer Science University of Pisa · Saarland Informatics Campus Saarland University & University of Amsterdam

Causal Representation Learning Representation Identifiability Sparse Identification of Nonlinear Dynamics ODE Discovery

Aug 13, 2026cs.LG

Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration

We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.

Sabin Roman, Ljupco Todorovski, Saso Dzeroski

Department of Knowledge Technologies, Jožef Stefan Institute · Faculty of Mathematics and Physics, University of Ljubljana

Sparse Identification of Nonlinear Dynamics Nonlinear System Identification Orthogonal Representation Learning ODE Discovery

Aug 1, 2026cs.LG

Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers

Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making. Yet high-fidelity simulations are prohibitively costly, and machine-learning surrogates can be opaque and encode assumptions about system dynamics, limiting generalizability. Pretrained transformers mapping synthetic ODE trajectories to equations offer interpretable alternatives, promising transfer without system-specific equation knowledge. Transferring them reliably to high-dimensional physical data, however, remains an open challenge. We develop a verifier-guided (VG) workflow around ODEFormer as a symbolic backbone, using dynamical and physical-admissibility criteria to select from a multi-trajectory candidate equation pool, enabling transfer. On canonical Van der Pol oscillators, VG outperforms the original ODEFormer workflow across held-out initial conditions. We then address vortex shedding, a phenomenon occurring in atmospheric and plasma systems of societal relevance, through coordinate reduction and symbolic discovery at fixed and varying Reynolds numbers. VG discovers fixed-parameter reduced-order equations that recover the fundamental shedding oscillator and higher harmonics without a wake-specific candidate library or prescribed Navier-Stokes structure, while the cross-parameter model generalizes to withheld regimes. Reconstruction fidelity alone did not determine symbolic discoverability, highlighting the importance of compatibility between latent dynamics and the backbone's pretraining distribution. This work establishes a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.

Farbod Faraji, Francesco Belardinelli

Department of Computing, Huxley Building, Imperial College London 180 Queen’s Gate, South Kensington, London SW7 2RH, United Kingdom

Nonlinear System Identification Autonomous Scientific Discovery ODE Discovery Symbolic Regression

Jul 31, 2026cs.LG

Dynamics-aware identification of governing equations from sparse and noisy data

Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this problem, we evaluate Koopman-based upsampling techniques implemented with dynamic mode decomposition (DMD), extended DMD (EDMD), and optimized DMD. These methods learn finite-dimensional approximations of Koopman evolution on selected observables and are used to interpolate and denoise snapshots inside the observed time window before derivative estimation and sparse regression. The empirical benchmark comprises two ODE systems, Lorenz-63 and Van der Pol, and three periodic PDE systems, Burgers, Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP), and linear advection-diffusion, over sparse and noisy sampling regimes. Polynomial EDMD gives the strongest ODE results, especially in coefficient accuracy. The PDE results are system-dependent: low-rank DMD-assisted reconstructions improve Burgers and advection-diffusion discovery, while the raw baseline (without upsampling) remains competitive for the Fisher-KPP data. A comparison against linear and smoothing-spline interpolation techniques shows that the selected Koopman-based preprocessors provide overall performance gains over these non-dynamical alternatives. We also demonstrate that DMD-assisted upsampling can stabilize Pareto-based non-oracle support-size selection. Overall, Koopman-based upsampling is best viewed as a dynamics-aware preprocessing step that can reduce derivative-estimation error when its observable representation and low-rank structure are appropriate for the data.

Pongpisit Thanasutives, Yoshinobu Kawahara

Center for Advanced Intelligence Project (AIP), RIKEN, Osaka, Japan · 2Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan

Koopman Operator Learning Sparse Identification of Nonlinear Dynamics PDE Discovery ODE Discovery Dynamic Mode Decomposition

Jul 20, 2026cs.LG

The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recovery

How the dynamical regime of the observed system affects equation discovery has mainly been investigated through comparisons across systems. However, such comparisons vary both the equations and the dynamics, confounding the effect of the regime with the difficulty of recovering the equations symbolically. We separate the two by varying the forcing of Lorenz-84, moving its fully observed post-transient trajectories through fixed-point, periodic, and chaotic regimes while preserving the equations' functional form. Within each regime, we separately vary the amount of data, the noise, and prior knowledge of which terms the equations contain. We then measure how well two complementary approaches, sparse regression over a fixed library of candidate functions (SINDy) and an evolutionary search over symbolic expression trees (PySR), recover the true equations' terms and coefficients. We find that recovery depends on whether the sampled states distinguish combinations of candidate functions: equations remain poorly recovered from fixed-point data even when the candidate set contains only the true terms. We link the effect of the dynamics on both algorithms to one object: the moment matrix of the candidate functions under the invariant measure of the regime. Small eigenvalues mark weakly distinguishable combinations of candidate functions: we show that more data, less noise, and more prior knowledge can mitigate the resulting recovery difficulties, while a zero eigenvalue makes distinct equations indistinguishable on the visited states. Hence, a more precise prior needs less informative data, with consequences for data collection, method design, and evaluation.

Matteo Gallo, Fabio Anselmi, Paolo Lazzari

University of Trieste, Trieste, Italy · National Institute of Oceanography and Applied Geophysics - OGS, Trieste, Italy · NBFC, National Biodiversity Future Center, Palermo, Italy

Dynamical Systems Parameter Identifiability Sparse Identification of Nonlinear Dynamics Scientific Discovery ODE Discovery Symbolic Regression

Jul 15, 2026cs.AI

Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System

Automatic scientific discovery has long been a goal of computational scholars - a machine that can discover nature's secrets on its own, moving computational systems beyond data-fitting tools toward the generation and refinement of mechanistic models of the universe. Recent advances in symbolic regression (SR) and large-language-model (LLM)-based agents suggest that such systems can recover equations from data, incorporate domain priors, and automate parts of the research workflow. However, most existing approaches either focus on narrow equation-discovery benchmarks or broad end-to-end automation pipelines, while biological systems remain comparatively underexplored. Here, we introduce the MEDA system, an LLM- and SR-powered agentic framework for discovering ordinary-differential-equation (ODE) models of biological and biologically inspired dynamical systems. MEDA retrieves background knowledge, defines admissible variables, generates mechanistic constraints, proposes candidate ODEs, and fits and evaluates them. We evaluate it across canonical model retrieval, reasoning-based extrapolation to unseen variants, and open-ended discovery, with and without experimental data. Across these settings, MEDA recovered the correct state variables, achieved strong structural recovery in retrieval and extrapolation tasks, and produced biologically plausible discovery-oriented models. Ablation and robustness analyses show that knowledge-guided formalization and mechanistic constraints are load-bearing components, whereas numerical fitting alone can preserve trajectory-compatible but biologically incorrect equations.

David Krongauz, Arad Zulti, Eran Segal +1

Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel · Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates +2

Dynamical Systems AI Agents for Scientific Discovery Autonomous Scientific Discovery ODE Discovery Symbolic Regression

Jul 1, 2026cs.LG

LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data

Mechanistic modeling via ordinary differential equations (ODEs) provides interpretable descriptions of complex dynamics and enables inference of underlying mechanisms, which is particularly valuable in clinical settings. However, in rare diseases, both the structure and parameters of the model are typically unknown, while individual-level data is scarce, noisy, heterogeneous, and subject to privacy constraints. In such settings, population-level summary statistics provide a practical privacy-preserving data representation, while capturing heterogeneity further requires modeling parameters as distributions rather than fixed values. Yet no existing method jointly discovers ODE structure and refines parameter distributions solely from summary statistics. We present AgentODE, an end-to-end framework that addresses this gap. An LLM proposes candidate ODE structures, while a tool-augmented inference agent iteratively refines parameter distributions through a diagnosis--update loop, operating on population-level summary statistics alone. We evaluate AgentODE on three benchmark problems across different fields and two clinical datasets, including the rare disease recessive dystrophic epidermolysis bullosa (RDEB), with only 231 observations across 46 patients. AgentODE recovers functionally consistent ODE structures across all settings, and experiments on RDEB demonstrates that in sparse and noisy data settings reasoning from summary statistics promotes mechanistically principled structure discovery, whereas baselines with individual-level data access recover implausible structures despite better predictive performance. AgentODE opens new possibilities for mechanistic modeling of rare diseases directly from population-level summary statistics, where data scarcity and privacy constraints have traditionally limited such analyses.

Hanning Yang, Meropi Karakioulaki, Lennart Purucker +3

Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Germany · Department of Dermatology, Medical Faculty and Medical Center, University of Freiburg, Germany · Prior Labs, University of Freiburg, Germany

Autonomous Scientific Discovery Large Language Model-Guided Scientific Discovery ODE Discovery

Jun 25, 2026cs.LG

Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs

Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning, yet the theoretical conditions under which a ground-truth ODE can be uniquely and stably identified from multiple solution observations remain largely undeveloped, and no quantitative analysis of the sample complexity of such learning tasks exists in the literature. To address this gap, we introduce the Hausdorff distance on solution sets as the natural metric for comparing differential equations, since it captures the worst-case separation between two equations over all admissible initial conditions and thus encodes the minimax structure of the identification problem. We establish identifiability bounds for governing ODEs across a wide class of structure equations--ranging from linear ODEs to nonlinear classes with Lipschitz (Hölder)-continuous vector fields--characterizing precisely when two distinct equations can be distinguished from solution data. Using this metric, we derive metric entropy estimates for the relevant ODE classes and analyze sample complexity bounds, quantifying how many solution observations are needed to reliably recover the governing equation.

Yang Pan, Helmut Bölcskei

Parameter Identifiability Sample Complexity Nonlinear System Identification Statistical Learning Theory ODE Discovery

Jun 23, 2026cs.LG

LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search

Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains. Existing approaches cast discovery as a static inference problem over fixed datasets, assuming that the observed trajectories are sufficiently informative. However, dynamical systems evolve over large state spaces, and limited data can make multiple equations observationally indistinguishable, leading to identifiability gaps and the recovery of incorrect governing equations. To address this, we introduce LLM-ACES, or LLM-guided Active Closed-loop Equation Search, a closed-loop framework that jointly optimizes symbolic hypothesis construction and adaptive data acquisition. In LLM-ACES, a large language model (LLM) proposes operator priors that partition the large search space into distinct regions, within which candidate equations are fit to the observed data. The disagreement among these candidates guides the acquisition of informative trajectories, creating a feedback loop that iteratively refines both the hypothesis space and the discovered dynamics. On 122 ODE systems spanning ODEBench and ODEBase, LLM-ACES achieves the lowest median NMSE, outperforming state-of-the-art baselines by several orders of magnitude while achieving a high symbolic accuracy of 46.2% and 52.4%, respectively. Our analysis further shows that LLM-ACES is sample-efficient, achieving better performance with one-tenth the data. Furthermore, LLM-ACES's feedback-driven data acquisition makes it robust to noise and recovers the correct symbolic structure, while baselines introduce spurious terms that fit the data locally but obscure the true governing relationships.

Nikhil Abhyankar, Sha Li, Sanchit Kabra +3

Virginia Tech

Nonlinear System Identification System Identification Autonomous Scientific Discovery Large Language Model-Guided Scientific Discovery ODE Discovery Symbolic Regression

May 27, 2026cs.CV

Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions

Bridging the gap between visual realism and physical understanding is a core challenge for video-based world models. We study the structural identifiability of continuous-time physical laws from raw pixels, focusing on whether an encoder-only pipeline can uniquely recover the parameters of second-order linear ODEs. We prove that a level-set slope-coverage condition ensures the learned latent space is locally affine to the true physical state, enabling exact parameter recovery. Our theory provides the first characterization of minimal data requirements across damping regimes, establishing that underdamped systems are identifiable from a single video clip, whereas other regimes require three diverse trajectories. We further introduce a variance-floor regularizer to stabilize the decoder-free objective and prevent latent collapse. Validated on synthetic and real-world data, our approach demonstrates that interpretable physical constants can be reliably estimated from video without the need for compute-intensive pixel reconstruction, ensuring both physical correctness and transparency. Code is available at https://github.com/wenjiewang3/PhysicsFromVideo.

Yuanyuan Wang, Wenjie Wang, Kun Zhang +1

Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · University of Melbourne, Melbourne, Australia · Carnegie Mellon University, Pittsburgh, USA

Parameter Identifiability Latent Dynamics Modeling System Identification Physical Reasoning in Video ODE Discovery

May 21, 2026cs.LG

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Complex dynamical systems governed by holomorphic maps such as

z^2 + c

exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these structures from data requires methods that respect the underlying complex-analytic geometry, yet Multi-Layer Perceptrons (MLPs) within Neural Ordinary Differential Equations (Neural ODEs) lack complex-analytic priors, violate the Cauchy--Riemann conditions, and function as opaque approximators incapable of yielding governing equations. We introduce Holomorphic KAN-ODE, a framework that replaces the MLP with a Kolmogorov-Arnold Network (KAN) whose learnable B-spline activations reside on network edges, and incorporates Cauchy--Riemann equations as a differentiable regularization to preserve holomorphic structure. We evaluate on six families of complex dynamical systems spanning polynomial and transcendental classes. With only 280 parameters (

16\times

fewer than the MLP baseline), the network achieves velocity-field

R^2 > 0.95

on all six systems, correctly identifies all six governing symbolic families through automatic spline-to-formula fitting, and reconstructs Julia set fractal boundaries with up to 98.0% agreement. Crucially, the model exhibits only 4% MSE degradation under 10% observation noise versus

15.2\times

for MLPs, and achieves 90.4% improvement in transfer learning from quadratic to cubic dynamics. While the MLP attains lower pointwise reconstruction error due to its larger capacity, the KAN uniquely provides interpretable symbolic equations, enforced holomorphic structure, and superior noise resilience, capabilities that are entirely absent in black-box architectures. These results establish KANs as a parameter-efficient, interpretable alternative to MLPs for physics-informed discovery of holomorphic dynamics.

Bhaskar Ranjan Karn, Dinesh Kumar

Nonlinear System Identification Complex-Valued Neural Networks Kolmogorov-Arnold Networks Chaotic Dynamical Systems Neural ODEs ODE Discovery

May 10, 2026cs.LG

Discovery of Nonlinear Dynamics with Automated Basis Function Generation

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel at discovering parsimonious models but require researchers to specify candidate basis functions a priori, a limitation that often leads to model failure when critical terms are omitted or when systems exhibit unconventional dynamics. Purely symbolic regression approaches offer unlimited flexibility but struggle with noise sensitivity and frequently produce overly complex, unstable equations. We present AutoSINDy, a hybrid Discovery-then-Solve framework that combines the exploratory power of symbolic regression with the robust sparsity-promoting capabilities of SINDy. Our method operates in three stages: (1) PySR-based symbolic regression discovers candidate functional forms from bootstrapped data chunks; (2) a curation pipeline decomposes, expands, and filters these expressions using collinearity analysis to construct a minimal yet comprehensive library; and (3) SINDy identifies sparse governing equations from this custom-tailored library. Extensive experiments across canonical nonlinear systems demonstrate that AutoSINDy consistently recovers ground-truth equations even under high observational noise, achieving a ground-truth recovery rate of 92.8% across all trials. Compared with standard SINDy using enriched libraries and standalone symbolic regression, AutoSINDy achieves higher predictive accuracy, superior generalization to unseen trajectories, and substantially lower symbolic complexity.

Mohammad Amin Basiri, Charles Nicholson

Data Science and Analytics Institute, University of Oklahoma, Norman, OK, USA · School of Industrial and Systems Engineering, University of Oklahoma, Norman, OK, USA

Sparse Identification of Nonlinear Dynamics Nonlinear System Identification Autonomous Scientific Discovery ODE Discovery Symbolic Regression

May 8, 2026cs.AI

Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation

Discovering governing differential equations from observational data is a fundamental challenge in scientific machine learning. Existing symbolic regression approaches rely primarily on quantitative metrics; however, real-world differential equation modeling also requires incorporating domain knowledge to ensure physical plausibility. To address this gap, we propose DoLQ, a method for discovering ordinary differential equations with LLM-based qualitative and quantitative evaluation. DoLQ employs a multi-agent architecture: a Sampler Agent proposes dynamic system candidates, a Parameter Optimizer refines equations for accuracy, and a Scientist Agent leverages an LLM to conduct both qualitative and quantitative evaluations and synthesize their results to iteratively guide the search. Experiments on multi-dimensional ordinary differential equation benchmarks demonstrate that DoLQ achieves superior performance compared to existing methods, not only attaining higher success rates but also more accurately recovering the correct symbolic terms of ground truth equations. Our code is available at https://github.com/Bon99yun/DoLQ.

Sum Kyun Song, Bong Gyun Shin, Jae Yong Lee

Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea · Department of AI Big Data, Daejin University, Pocheon-si, Republic of Korea.

AI Agents for Scientific Discovery Autonomous Scientific Discovery Large Language Model-Guided Scientific Discovery ODE Discovery Symbolic Regression

May 7, 2026cs.LG

PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability

Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements. A known issue is the ill-conditioned nature of the inverse problem, which frequently produces multiple mathematical models that fit the data similarly well. One path to address this issue is by incorporating known hypotheses and constraints into the training phase beforehand. While this approach effectively reduces the search space, it still results in multiple candidate models, forcing practitioners to rely on post-hoc manual filtering based on their own domain expertise. A recent approach incorporates structural `skeletons' inspired by characteristic curves (CCs), defining a hypothesis-driven methodology. In this methodology, practitioners define a skeleton, which is associated with a family of ordinary differential equations (ODEs), and then add their hypotheses and priors based on their domain knowledge to refine the obtained model iteratively. An important advantage of this approach is that some skeletons have demonstrable structural identifiability properties, which are useful for checking whether the skeleton is correct or should be discarded. Furthermore, this formalism enables the use of multiple equation discovery paradigms due to its modularity (such as neural networks, symbolic regression, and sparse regression). In this work, we present the Python library PyCC, which condenses these efforts into a flexible tool that allows researchers and engineers to seamlessly define their skeletons and hypotheses to discover ODEs from time-dependent data.

Federico J. Gonzalez

Physics Institute of Rosario (IFIR), CONICET-UNR, Blvd. 27 de Febrero 210 Bis, Rosario, S2000EZP, Argentina.

Autonomous Scientific Discovery Inverse Problems ODE Discovery

Apr 22, 2026cs.LG

Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By using orthogonal sinusoidal test functions inspired by their prevalence in Modulating Function-based system identification, the weak-form sparse regression problem reduces to a regression over Fourier coefficients. Dominant frequencies are then selected via multitaper estimation of the frequency spectrum of the data. This formulation unifies weak-form learning and spectral estimation within a compact and flexible framework. We illustrate the effectiveness of this approach in numerical experiments across multiple chaotic and hyperchaotic ODE benchmarks.

Zhiheng Chen, Urban Fasel, Anastasia Bizyaeva

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 14850 · Department of Aeronautics, Imperial College London, London, United Kingdom

Sparse Identification of Nonlinear Dynamics Nonlinear System Identification System Identification ODE Discovery

Apr 17, 2026cs.LG

Neuro-Symbolic ODE Discovery with Latent Grammar Flow

Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a neuro-symbolic generative framework for discovering ordinary differential equations from data. LGF embeds equations as grammar-based representations into a discrete latent space and forces semantically similar equations to be positioned closer together with a behavioural loss. Then, a discrete flow model guides the sampling process to recursively generate candidate equations that best fit the observed data. Domain knowledge and constraints, such as stability, can be either embedded into the rules or used as conditional predictors.

Karin Yu, Eleni Chatzi, Georgios Kissas

Institute of Structural Engineering, ETH Zurich, Zurich, Switzerland · ETH AI Center, ETH Zurich, Zurich, Switzerland · Swiss Data Science Center, Zurich, Switzerland

Autonomous Scientific Discovery Neurosymbolic Learning ODE Discovery Symbolic Regression