相关论文: SymPlex: A Structure-Aware Transformer for Symboli…
This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search of combinatorial spaces. We introduce SIGS, a neuro-symbolic…
Many real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
Deep models have recently emerged as promising tools to solve partial differential equations (PDEs), known as neural PDE solvers. While neural solvers trained from either simulation data or physics-informed loss can solve PDEs reasonably…
Reinforcement learning (RL) has seen significant success across various domains, but its adoption is often limited by the black-box nature of neural network policies, making them difficult to interpret. In contrast, symbolic policies allow…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural…
Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we…
Optimization time integrators are effective at solving complex multi-physics problems including deformable solids with non-linear material models, contact with friction, strain limiting, etc. For challenging problems, Newton-type optimizers…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
In this presentation, we introduce our constraint-based repair approach, called SymDefFix. SymDefFix is based on ExtractFix [3] and replaces the dynamic analysis steps of ExtractFix to detect the error and find the potential fix locations…