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.
arXiv:2607. 13608v1 Announce Type: new Abstract: 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.
By David Krongauz, Arad Zulti, Eran Segal, Teddy Lazebnik
Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate.
arXiv:2606. 06295v1 Announce Type: new Abstract: Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial.
By Rishal Aggarwal, David Ryan Koes, Nicholas M. Boffi, Eric Vanden-Eijnden
arXiv:2608. 02662v1 Announce Type: cross Abstract: Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making.
By Farbod Faraji, Francesco Belardinelli
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
By Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.
By Simon De Reuver, Tamas Kristof Toth, Teddy Lazebnik
arXiv:2606. 09638v1 Announce Type: new Abstract: Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena.
By Siyu Lou, Hao Xu, Wenguan Wang, Lu Lu, Hao Sun, Yang Liu, Linfeng Zhang, Dongxiao Zhang, Yuntian Chen
arXiv:2608. 05120v1 Announce Type: new Abstract: Kinetic model discovery is a central challenge in chemical engineering, as accurate rate expressions are essential for understanding and controlling chemical and biological processes.
By Roberto Aliaga Medina, Paulina Quintanilla, Antonio del Rio Chanona
The paper presents a probabilistic symbolic regression framework that models mathematical expressions as ensembles of symbolic trees, using a regularizing prior to control complexity and an Occam’s window-based posterior to capture uncertainty across plausible models. It provides theoretical guarantees on posterior concentration, including near‑parametric rates when an exact finite formula exists and oracle results under misspecification. Empirical results show the method outperforms state‑of‑the‑art competitors in predictive accuracy, symbolic complexity, and structural recovery on benchmark scientific equations and a materials discovery task.
By Somjit Roy, Pritam Dey, Bani K. Mallick, Debdeep Pati
Kinetic model discovery is a central challenge in chemical engineering, as accurate rate expressions are essential for understanding and controlling chemical and biological processes. Symbolic regression (SR) has emerged as a powerful data-driven approach for identifying interpretable kinetic models, but usually operates without domain knowledge, often exploring physicochemically implausible models.
arXiv:2606. 20467v1 Announce Type: new Abstract: Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values.
By Zongmin Yu, Liu Yang