Related papers: A Physics-Constrained Neural Differential Equation…

Machine learning is gaining growing momentum in various recent models for the dynamic analysis of information flows in data communications networks. These preliminary models often rely on off-the-shelf learning models to predict from…

Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle…

We have analyzed phenology data and protein configurations from molecular dynamics simulations with the nonlinear forecasting method proposed by May and Sugihara. Our primary focus in this work is to characterize the dynamic state of a…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time…

As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…

Data-driven methods have become increasingly more prominent for musculoskeletal modelling due to their conceptually intuitive simple and fast implementation. However, the performance of a pre-trained data-driven model using the data from…

Recent advances in deep learning have driven rapid progress in time series forecasting, yet many state-of-the-art models continue to struggle with robust performance in real-world applications, even when they achieve strong results on…

Deep neural networks (NNs) are known to lack uncertainty estimates and struggle to incorporate new data. We present a method that mitigates these issues by converting NNs from weight space to function space, via a dual parameterization.…

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…

Physics-based numerical models have been the bedrock of atmospheric sciences for decades, offering robust solutions but often at the cost of significant computational resources. Deep learning (DL) models have emerged as powerful tools in…

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…

We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of…

Central to Earth observation is the trade-off between spatial and temporal resolution. For temperature, this is especially critical because real-world applications require high spatiotemporal resolution data. Current technology allows for…