Related papers: MPINeuralODE: Multiple-Initial-Condition Physics-I…

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Using vanilla NeuralODEs to model large and/or complex systems often fails due two reasons: Stability and convergence. NeuralODEs are capable of describing stable as well as instable dynamic systems. Selecting an appropriate numerical…

Miniature robotic blimps, as one type of lighter-than-air aerial vehicles, have attracted increasing attention in the science and engineering community for their enhanced safety, extended endurance, and quieter operation compared to…

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical…

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical…

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Dynamic astrophysical phenomena are predominantly described by differential equations, yet our understanding of these systems is constrained by our incomplete grasp of non-linear physics and scarcity of comprehensive datasets. As such,…

Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to…

Physics-informed neural networks (PINNs) have proven a suitable mathematical scaffold for solving inverse ordinary (ODE) and partial differential equations (PDE). Typical inverse PINNs are formulated as soft-constrained multi-objective…

Exploiting low-precision computations has become a standard strategy in deep learning to address the growing computational costs imposed by ever larger models and datasets. However, naively performing all computations in low precision can…