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Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…
Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…
We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically…
Control of fluid dynamics at the micrometer scale is essential to emulsion science and materials design, which is ubiquitous in everyday life and is frequently encountered in industrial applications. Most studies on multiphase flow focus on…
This paper highlights several properties of large urban networks that can have an impact on machine learning methods applied to traffic signal control. In particular, we show that the average network flow tends to be independent of the…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and the desired output of the model on the current training…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
In this article we detail the use of machine learning for spatiotemporally dynamic turbulence model classification and hybridization for the large eddy simulations (LES) of turbulence. Our predictive framework is devised around the…
Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either…
Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…
The directed motion of active colloids is governed by spatial variations in surface chemistry and interfacial stress, yet these properties remain extremely difficult to measure directly. We introduce a physics-informed neural network…
Recently, building on the foundation of neural radiance field, various techniques have emerged to learn unsigned distance fields (UDF) to reconstruct 3D non-watertight models from multi-view images. Yet, a central challenge in UDF-based…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically…
Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…
The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…