Related papers: Physics-Informed Neural ODEs with Scale-Aware Resi…

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…

Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

We introduce NeuroPINNs, a neuroscience-inspired extension of Physics-Informed Neural Networks (PINNs) that incorporates biologically motivated spiking neuron models to achieve energy-efficient PDE solving. Unlike conventional PINNs, which…

Foundation models have transformed language, vision, and time series data analysis, yet progress on dynamic predictions for physical systems remains limited. Given the complexity of physical constraints, two challenges stand out. $(i)$…

AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…

In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…

Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron…

A novel physics-informed operator learning technique based on spectral methods is introduced to model the complex behavior of heterogeneous materials. The Lippmann-Schwinger operator in Fourier space is employed to construct physical…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce…

We study learning of continuous-time inventory dynamics under stochastic demand and quantify when structure helps or hurts forecasting of the bullwhip effect. BULL-ODE compares a fully learned Neural ODE (NODE) that models the entire…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…