Related papers: Learning Hamiltonian Dynamics at Scale: A Differen…

Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in…

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the…

Recurrent Neural Networks (RNNs) have been widely used in natural language processing and computer vision. Among them, the Hierarchical Multi-scale RNN (HM-RNN), a kind of multi-scale hierarchical RNN proposed recently, can learn the…

Real-world networks have high-order relationships among objects and they evolve over time. To capture such dynamics, many works have been studied in a range of fields. Via an in-depth preliminary analysis, we observe two important…

Predicting optoelectronic properties of large-scale atomistic systems under realistic conditions is crucial for rational materials design, yet computationally prohibitive with first-principles simulations. Recent neural network models have…

Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…

Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle…

Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work,…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…

A deep understanding of the intricate interactions between particles within a system is a key approach to revealing the essential characteristics of the system, whether it is an in-depth analysis of molecular properties in the field of…

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

We propose an effective and lightweight learning algorithm, Symplectic Taylor Neural Networks (Taylor-nets), to conduct continuous, long-term predictions of a complex Hamiltonian dynamic system based on sparse, short-term observations. At…

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…

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 work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also…

This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…