相关论文: Learning Hamiltonian Dynamics at Scale: A Differen…

We construct the first physics-informed neural-network (PINN) surrogates for relativistic magnetohydrodynamics (RMHD) using a hybrid PDE and data-driven workflow. Instead of training for the conservative form of the equations, we work with…

Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…

This paper proposes two projector-based Hopfield neural network (HNN) estimators for online, constrained parameter estimation under time-varying data, additive disturbances, and slowly drifting physical parameters. The first is a…

We present a fast and scalable framework, leveraging graph neural networks (GNNs) and hierarchical matrix ($\mathcal{H}$-matrix) techniques, for simulating large-scale particulate suspensions, which have broader impacts across science and…

Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Weather Forecasting is an attractive challengeable task due to its influence on human life and complexity in atmospheric motion. Supported by massive historical observed time series data, the task is suitable for data-driven approaches,…

Preserving geometric structure is important in learning. We propose a unified class of geometry-aware architectures that interleave geometric updates between layers, where both projection layers and intrinsic exponential map updates arise…

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

Recent years have been marked with the fast-pace diversification and increasing ubiquity of machine learning applications. Yet, a firm theoretical understanding of the surprising efficiency of neural networks to learn from high-dimensional…

We propose a \emph{hybrid} real- and complex-valued \emph{neural network} (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…

Engineering desired Hamiltonian in quantum many-body systems is essential for applications such as quantum simulation, computation and sensing. Conventional quantum Hamiltonian engineering sequences are designed using human intuition based…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…