Related papers: NeuralODEs for VLEO simulations: Introducing therm…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Atmospheric turbulence degrades the performance of free-space optical (FSO) communication and remote sensing systems by introducing phase and intensity distortions. While a majority of research focuses on mitigating these effects to ensure…

We propose a neural network architecture, called TransNet, that combines planning and model learning for solving Partially Observable Markov Decision Processes (POMDPs) with non-uniform system dynamics. The past decade has seen a…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing…

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of…

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Thermal and magneto-thermal simulations are an important tool for advancing understanding of neutron stars, as they allow us to compare models of their internal structure and physical processes against observations constraining macroscopic…

Context. Computing spectra from 3D simulations of stellar atmospheres when allowing for departures from local thermodynamic equilibrium (non-LTE) is computationally very intensive. Aims. We develop a machine learning based method to speed…

We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…