Related papers: Adaptable Hamiltonian neural networks
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…
Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…
Rapid development of big data and high-performance computing have encouraged explosive studies of deep learning in geoscience. However, most studies only take single-type data as input, frittering away invaluable multisource, multi-scale…
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…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Heterogeneous graphs (HGs) are common in real-world scenarios and often exhibit heterophily. However, most existing studies focus on either heterogeneity or heterophily in isolation, overlooking the prevalence of heterophilic HGs in…
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…
In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…
The computational complexity of calculating phase diagrams for multi-parameter models significantly limits the ability to select parameters that correspond to experimental data. This work presents a machine learning method for solving the…
Human learning is a complex phenomenon that requires adaptive processes across a range of temporal and spacial scales. While our understanding of those processes at single scales has increased exponentially over the last few years, a…
Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…
Neurochaos Learning (NL) is a brain-inspired classification framework that employs chaotic dynamics to extract features from input data and yields state of the art performance on classification tasks. However, NL requires the tuning of…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
The H\"uckel Hamiltonian is an incredibly simple tight-binding model famed for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only…
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…
Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited…
Accurate forecasting of multivariate time series data remains a formidable challenge, particularly due to the growing complexity of temporal dependencies in real-world scenarios. While neural network-based models have achieved notable…
Conventional hyperparameter optimization methods are computationally intensive and hard to generalize to scenarios that require dynamically adapting hyperparameters, such as life-long learning. Here, we propose an online hyperparameter…
Development of next-generation electronic devices for applications call for the discovery of quantum materials hosting novel electronic, magnetic, and topological properties. Traditional electronic structure methods require expensive…
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…