Interpretable Neural PDE Solvers using Symbolic Frameworks
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, while these methods have demonstrated state-of-the-art performance in both accuracy and computational efficiency, a significant challenge remains in their interpretability. Most existing methodologies prioritize predictive accuracy over clarity in the underlying mechanisms driving the model's decisions. Interpretability is crucial for trustworthiness and broader applicability, especially in scientific and engineering domains where neural PDE solvers might see the most impact. In this context, a notable gap in current research is the integration of symbolic frameworks (such as symbolic regression) into these solvers. Symbolic frameworks have the potential to distill complex neural operations into human-readable mathematical expressions, bridging the divide between black-box predictions and solutions.
Code (0)
등록된 구현이 없습니다.
Tasks
Computational EfficiencySymbolic RegressionSimilar Papers 제목 키워드 기반
A Differentiable Integer Linear Programming Solver for Explanation-Based Natural Language Inference
Integer Linear Programming (ILP) has been proposed as a formalism for encoding precise structural and semantic constraints for Natural Language Inference (NLI). However, traditional ILP frameworks are non-differentiable,…
Natural Language InferenceGoing Beyond Approximation: Encoding Constraints for Explainable Multi-hop Inference via Differentiable Combinatorial Solvers
Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable …
Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach
Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LL…
Logical ReasoningAbductive Reasoning with Probabilistic Commonsense
Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense …
Formal LogicDiscovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions
Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human expe…
regressionSymbolic Regression