Related papers: Interpretable Neural PDE Solvers using Symbolic Fr…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

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…

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…

Deep neural networks have demonstrated remarkable performance across various domains, yet their decision-making processes remain opaque. Although many explanation methods are dedicated to bringing the obscurity of DNNs to light, they…

Interpretable representations are the backbone of many explainers that target black-box predictive systems based on artificial intelligence and machine learning algorithms. They translate the low-level data representation necessary for good…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

In cognitive decoding, researchers aim to characterize a brain region's representations by identifying the cognitive states (e.g., accepting/rejecting a gamble) that can be identified from the region's activity. Deep learning (DL) methods…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…

Learning efficient and interpretable policies has been a challenging task in reinforcement learning (RL), particularly in the visual RL setting with complex scenes. While neural networks have achieved competitive performance, the resulting…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Transformer models have become state-of-the-art in decoding stimuli and behavior from neural activity, significantly advancing neuroscience research. Yet greater transparency in their decision-making processes would substantially enhance…

Natural language is inherently a discrete symbolic representation of human knowledge. Recent advances in machine learning (ML) and in natural language processing (NLP) seem to contradict the above intuition: discrete symbols are fading…

Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

The ability of deep learning (DL) to improve the practice of medicine and its clinical outcomes faces a looming obstacle: model interpretation. Without description of how outputs are generated, a collaborating physician can neither resolve…

Differentiable Programming for scientific machine learning (SciML) has recently seen considerable interest and success, as it directly embeds neural networks inside PDEs, often called as NeuralPDEs, derived from first principle physics.…