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Recurrent Neural Networks (RNNs) are widely used for sequential processing but face fundamental limitations with continual inference due to state saturation, requiring disruptive hidden state resets. However, reset-based methods impose…
Surrogate models of numerical relativity simulations of merging black holes provide the most accurate tools for gravitational-wave data analysis. Neural network-based surrogates promise evaluation speedups, but their accuracy relies on…
Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic…
A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Recently, several optimization methods have been successfully applied to the hyperparameter optimization of deep neural networks (DNNs). The methods work by modeling the joint distribution of hyperparameter values and corresponding error.…
When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time dependent problems in engineering…
This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…
The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…
We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…
Accurately modeling the spatio-temporal dynamics of blast wave propagation remains a longstanding challenge due to its highly nonlinear behavior, sharp gradients, and burdensome computational cost. While machine learning-based surrogate…
Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the…
In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data,…
Neural networks are increasingly used as fast surrogate models across various domains, but unconstrained predictions can violate physical, operational, or safety requirements. We propose SnareNet, a feasibility-controlled architecture to…
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…
Spiking Neural Networks (SNNs) exhibit exceptional energy efficiency on neuromorphic hardware due to their sparse activation patterns. However, conventional training methods based on surrogate gradients and Backpropagation Through Time…
In constraint learning, we use a neural network as a surrogate for part of the constraints or of the objective function of an optimization model. However, the tractability of the resulting model is heavily influenced by the size of the…