Closed-form Symbolic Solutions: A New Perspective on Solving Partial Differential Equations
원문 초록
Solving partial differential equations (PDEs) in Euclidean space with closed-form symbolic solutions has long been a dream for mathematicians. Inspired by deep learning, Physics-Informed Neural Networks (PINNs) have shown great promise in numerically solving PDEs. However, since PINNs essentially approximate solutions within the continuous function space, their numerical solutions fall short in both precision and interpretability compared to symbolic solutions. This paper proposes a novel framework: a closed-form \textbf{Sym}bolic framework for \textbf{PDE}s (SymPDE), exploring the use of deep reinforcement learning to directly obtain symbolic solutions for PDEs. SymPDE alleviates the challenges PINNs face in fitting high-frequency and steeply changing functions. To our knowledge, no prior work has implemented this approach. Experiments on solving the Poisson's equation and heat equation in time-independent and spatiotemporal dynamical systems respectively demonstrate that SymPDE can provide accurate closed-form symbolic solutions for various types of PDEs.
함께 살펴볼 논문
공통 태그를 근거로 연결했습니다. 실제 인용 관계나 논문의 우수성을 뜻하지 않습니다.
Deep Reinforcement Learning with Gradient Eligibility Traces
Generalized Adaptive Transfer Network: Enhancing Transfer Learning in Reinforcement Learning Across Domains
TRACED: Transition-aware Regret Approximation with Co-learnability for Environment Design
Adaptive Action Duration with Contextual Bandits for Deep Reinforcement Learning in Dynamic Environments
Learning to Explore in Diverse Reward Settings via Temporal-Difference-Error Maximization
DR-SAC: Distributionally Robust Soft Actor-Critic for Reinforcement Learning under Uncertainty
토론
이 논문과 연결된 포럼 글이 아직 없습니다.