Related papers: Discovering Interpretable Physical Models using Sy…
We introduce a robust, interpretable machine learning (ML) framework that combines numerical regression for high-accuracy predictions with symbolic regression to uncover the underlying physics. This hybrid approach effciently derives…
Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve…
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…
Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness, however their analytical…
Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
Symbolic Regression (SR) searches for mathematical expressions which best describe numerical datasets. This allows to circumvent interpretation issues inherent to artificial neural networks, but SR algorithms are often computationally…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
Symbolic regression (SR) has emerged as a powerful tool for automated scientific discovery, enabling the derivation of governing equations from experimental data. A growing body of work illustrates the promise of integrating domain…
Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is…
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the…
The discovery of constitutive laws for complex materials has historically faced a dichotomy between high-fidelity data-driven approaches, which demand prohibitive full-field experimental data, and traditional engineering fitting, which…
Symbolic regression (SR) is an emerging branch of machine learning focused on discovering simple and interpretable mathematical expressions from data. Although a wide-variety of SR methods have been developed, they often face challenges…
Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…