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08/24/2023
Easy attention: A simple self-attention mechanism for Transformers
To improve the robustness of transformer neural networks used for tempor...
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04/24/2023
On the lifting and reconstruction of dynamical systems with multiple attractors
The Koopman operator provides a linear perspective on non-linear dynamic...
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04/04/2023
Global Identifiability Analysis of Statistical Models using an Information-Theoretic Estimator in a Bayesian Framework
An information-theoretic estimator is proposed to assess the global iden...
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06/30/2022
A Non-intrusive Approach for Physics-constrained Learning with Application to Fuel Cell Modeling
A data-driven model augmentation framework, referred to as Weakly-couple...
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09/20/2021
`Basic' Generalization Error Bounds for Least Squares Regression with Well-specified Models
This note examines the behavior of generalization capabilities - as defi...
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09/15/2021
Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems
Simulations of complex physical systems are typically realized by discre...
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09/15/2021
Disentangling Generative Factors of Physical Fields Using Variational Autoencoders
The ability to extract generative parameters from high-dimensional field...
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09/14/2021
Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries
Numerical solutions of partial differential equations (PDEs) require exp...
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03/25/2021
A formal proof of the Lax equivalence theorem for finite difference schemes
The behavior of physical systems is typically modeled using differential...
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01/27/2021
Variational Encoders and Autoencoders : Information-theoretic Inference and Closed-form Solutions
This work develops problem statements related to encoders and autoencode...
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02/25/2020
Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces
Koopman decomposition is a non-linear generalization of eigen decomposit...
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12/23/2019
Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
A data-driven framework is proposed for the predictive modeling of compl...
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06/09/2019
Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
The Koopman operator has emerged as a powerful tool for the analysis of ...
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05/30/2019
Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
An approximation model based on convolutional neural networks (CNNs) is ...
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05/31/2018
Long-time predictive modeling of nonlinear dynamical systems using neural networks
We study the use of feedforward neural networks (FNN) to develop models ...
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03/25/2018