The paper introduces HER-PDE, a scientific-agent framework that simultaneously discovers partial differential equation (PDE) structures and their unknown spatial coefficient fields. Using two noisy trajectories from different excitations, the agent generates expression-tree hypotheses, evaluates them via a Hypothesis Evaluation Interface that only estimates declared fields, and refines candidates through bidirectional cross-excitation transfer. In controlled experiments on five two-dimensional systems with Gaussian noise, HER-PDE accurately recovers the governing operators and attains a median Pearson correlation of ~0.85 and a median relative L2 error of ~0.28 for nine unknown coefficient fields.
arXiv:2610.26963v1 Announce Type: cross Abstract: Discovering governing partial differential equations (PDEs) from observed data is a central inverse problem in computational science and engineering:...
The paper introduces SED-MCTS, a Monte Carlo tree search method that enhances PDE solution discovery by distilling structural experience from evaluated expressions. Unlike previous approaches that rely on a single terminal score, SED-MCTS uses counterfactual subtree interventions to estimate local structural contributions, guiding the search toward reliable construction edges and preserving useful components in a structural archive. The method extends naturally to coupled multiphysics systems and demonstrates improved performance, efficiency, and robustness across diverse PDE benchmarks, especially under noisy or scarce observations.
arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.
arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.
arXiv:2608. 04872v1 Announce Type: cross Abstract: Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar score and a single prompt.
Symbolic regression aims to discover closed-form equations from data, but existing LLM-guided methods often rely on a unified proposal loop that compresses heterogeneous search failures into a scalar score and a single prompt. We propose A-SR, a self-evolving agentic framework that shifts the control unit from expression edits to role-conditioned evidence views.
arXiv:2503.19081v2 Announce Type: replace Abstract: Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PD...
arXiv:2506. 20181v2 Announce Type: replace Abstract: We study operator relevance in data-driven partial differential equation (PDE) discovery.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
MOSAIC is a sparse temporal variational autoencoder that merges causal representation learning with support recovery to identify interpretable latent modules in scientific time series. It leverages regime‑conditioned temporal variation to discover latent variables and uses an additive decoder to recover a sparse set of observations linked to each latent, providing module‑level interpretability. The method offers theoretical guarantees for ANOVA main‑effect identifiability under smooth mixing functions and demonstrates empirical success across diverse domains such as RNA dynamics, solar wind, ENSO climate, industrial process control, and synthetic tokamak data.
arXiv:2608. 02662v1 Announce Type: cross Abstract: Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making.
arXiv:2608.22504v1 Announce Type: new Abstract: Existing AI-for-PDE benchmarks primarily assess models in terms of predictive or approximation accuracy. In physics research, however, AI outputs often...