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In reacting flow systems, thermoacoustic instability characterized by high amplitude pressure fluctuations, is driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. When the underlying…
The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs,…
Designing network parameters that can effectively represent complex networks is of significant importance for the analysis of time-varying complex networks. This paper introduces a novel thermodynamic framework for analyzing complex…
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…
The troposphere is one of the atmospheric layers where most weather phenomena occur. Temperature variations in the troposphere, especially at 500 hPa, a typical level of the middle troposphere, are significant indicators of future weather…
We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and…
We present three different neural network algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows…
In this paper, we propose an innovative learning-based channel prediction scheme so as to achieve higher prediction accuracy and reduce the requirements of huge amounts and strict sequential format of channel data. Inspired by the idea of…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…
Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…
Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
Dynamic astrophysical phenomena are predominantly described by differential equations, yet our understanding of these systems is constrained by our incomplete grasp of non-linear physics and scarcity of comprehensive datasets. As such,…
In astrophysical simulations, nuclear reacting flows pose computational challenges due to the stiffness of reaction networks. We introduce neural network-based surrogate models using the DeePODE framework to enhance simulation efficiency…
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
We improve the accuracy of Guidance & Control Networks (G&CNETs), trained to represent the optimal control policies of a time-optimal transfer and a mass-optimal landing, respectively. In both cases we leverage the dynamics of the…