Related papers: Sparse Symplectically Integrated Neural Networks

Understanding what makes high-dimensional data learnable is a fundamental question in machine learning. On the one hand, it is believed that the success of deep learning lies in its ability to build a hierarchy of representations that…

Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous.…

Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns…

In this manuscript, we propose efficient stochastic semi-explicit symplectic schemes tailored for nonseparable stochastic Hamiltonian systems (SHSs). These semi-explicit symplectic schemes are constructed by introducing augmented…

Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…

State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based…

Long Short-Term Memory (LSTM) has achieved state-of-the-art performances on a wide range of tasks. Its outstanding performance is guaranteed by the long-term memory ability which matches the sequential data perfectly and the gating…

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

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…

Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolving discontinuities. To address these limitations, we propose…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…

Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…

Spiking Neural Networks (SNNs) represent the forefront of neuromorphic computing, promising energy-efficient and biologically plausible models for complex tasks. This paper weaves together three groundbreaking studies that revolutionize SNN…

Recurrent neural networks (RNNs) are powerful and effective for processing sequential data. However, RNNs are usually considered "black box" models whose internal structure and learned parameters are not interpretable. In this paper, we…