Data Enrichment for Symbolic Regression Using Diffusion Models

• URL: http://arxiv.org/abs/2606.00988v1
• Date: Sun, 31 May 2026 04:03:32 GMT
• Title: Data Enrichment for Symbolic Regression Using Diffusion Models
• Abstract summary: We introduce a physics-guided latent fluidity diffusion framework for SR models.<n>We evaluate the approach on heat conduction, incompressible Navier-Stokes flow, and a moving single-mass Newtonian gravitational potential.
• Score: 4.817429789586127
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations. However, despite its promise, its reliability degrades sharply when spatiotemporal measurements are sparse, noisy, or physically incomplete, as commonly occurring in practice. Data enrichment (DE) has been shown to be able to mitigate this limitation, yet additional samples can mislead equation discovery unless they preserve the physical structure of the target system. Such implication of DE requires narrow domain expertise as well as technical fluidity, highly limiting its practical usefulness. In this study, we introduce a physics-guided latent diffusion framework for DE for down the line SR models. The proposed framework combines a variational autoencoder, a conditional latent diffusion model, and a physics-informed residual corrector to complete sparse observations with synthetic fields constrained by governing relations. We evaluate the approach on heat conduction, incompressible Navier-Stokes flow, and a moving single-mass Newtonian gravitational potential, using GPLearn, DEAP, and PySR as downstream SR backends. Our results reveal that physics-corrected enrichment consistently improves recovery in sparse regimes across physical dynamics and SR models. These results show that generative enrichment can strengthen equation discovery without additional domain expertise.

Related papers

• Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources [46.07145155913717]
  We exploit PINNs as Residual Least Squares (RLS) methods and show that this perspective enables direct treatment of Dirac delta terms.<n>We show that while integrating out the Dirac delta in PINNs causes residuals to fail to converge to zero, RBF-RLS consistently provides good forward and inverse solutions to transport problems.
  arXiv  Detail & Related papers  (2026-06-10T22:53:43Z)
• Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification [5.8001568807112855]
  Recent advances in machine learning provide a means of near-real-time solution to partial differential equations (PDEs)<n>We construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates.
  arXiv  Detail & Related papers  (2026-06-10T04:27:23Z)
• PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics [14.400502760340862]
  PDE-governed fields from sparse and irregular measurements are challenging due to their ill-posed nature.<n>We propose PerFlow, a rectified Flow for efficient sparse reconstruction and uncertainty quantification oftemporal dynamics.<n> Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics, while enabling efficient conditional sampling.
  arXiv  Detail & Related papers  (2026-05-05T09:19:09Z)
• EFF-Grasp: Energy-Field Flow Matching for Physics-Aware Dexterous Grasp Generation [54.09734511705173]
  EFF-Grasp is a Flow-Matching synthesis-based framework for physics-aware dexterous grasp generation.<n>We reformulate grasp as a deterministic ordinary differential equation (ODE) process, which enables efficient and stable generation through smooth probability flows.<n> EFF-Grasp achieves superior performance in grasp quality and physical feasibility, while requiring substantially fewer sampling steps than diffusion-based baselines.
  arXiv  Detail & Related papers  (2026-03-17T06:11:56Z)
• PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations [0.496981595868944]
  Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime.<n>We introduce textbfPHDME, a port-Hamiltonian diffusion framework designed for emphsparse observations and emphincomplete physics.<n>Experiments on PDE benchmarks and a real-world spring system show improved accuracy and physical consistency under data scarcity.
  arXiv  Detail & Related papers  (2026-01-29T03:53:48Z)
• Weighted Stochastic Differential Equation to Implement Wasserstein-Fisher-Rao Gradient Flow [0.0]
  A promising line of work leverages tools from information geometry to augment diffusion-based samplers with mass reweighting mechanisms.<n>Our work provides a preliminary but rigorous investigation of WFR-based sampling dynamics, and aims to clarify their theoretical structure as a foundation for future developments.
  arXiv  Detail & Related papers  (2025-12-19T18:31:27Z)
• Training-Free Stein Diffusion Guidance: Posterior Correction for Sampling Beyond High-Density Regions [46.59494117137471]
  Training free diffusion guidance provides a flexible way to leverage off-the-shelf classifiers without additional training.<n>We introduce Stein Diffusion Guidance (SDG), a novel training-free framework grounded in a surrogate SOC objective.<n>Experiments on molecular low-density sampling tasks suggest that SDG consistently surpasses standard training-free guidance methods.
  arXiv  Detail & Related papers  (2025-07-07T21:14:27Z)
• Physically Interpretable Representation and Controlled Generation for Turbulence Data [39.42376941186934]
  This paper proposes a data-driven approach to encode high-dimensional scientific data into low-dimensional, physically meaningful representations.<n>We validate our approach using 2D Navier-Stokes simulations of flow past a cylinder over a range of Reynolds numbers.
  arXiv  Detail & Related papers  (2025-01-31T17:51:14Z)
• Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics [11.919291977879801]
  Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Diffusion models have shown promise as potent generative tools for solving inverse problems.
  arXiv  Detail & Related papers  (2024-06-19T15:55:12Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
  We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE) It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2023-10-10T08:52:16Z)
• PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers [40.097474800631]
  Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Deep neural network based surrogates have gained increased interest.
  arXiv  Detail & Related papers  (2023-08-10T17:53:05Z)
• Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data [0.0]
  We propose to use Bayesian neural networks (BNN) in order to recover the full system states from measurement data. We show that it is possible to accurately capture physics of varying complexity without overfitting. We demonstrate our approach on a handful of example applied to physics and non-linear dynamics.
  arXiv  Detail & Related papers  (2021-08-05T19:43:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.