no code implementations • 28 Jun 2024 • Wenqian Chen, Amanda A. Howard, Panos Stinis

In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence speed of residuals at different training points, where the slowest convergence speed dominates the overall solution convergence.

1 code implementation • 28 Jun 2024 • Amanda A. Howard, Bruno Jacob, Sarah H. Murphy, Alexander Heinlein, Panos Stinis

Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning.

no code implementations • 15 Jan 2024 • Alexander Heinlein, Amanda A. Howard, Damien Beecroft, Panos Stinis

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs).

no code implementations • 1 Dec 2023 • Youngeun Kim, Adar Kahana, Ruokai Yin, Yuhang Li, Panos Stinis, George Em Karniadakis, Priyadarshini Panda

In this work, we delve into the role of skip connections, a widely used concept in Artificial Neural Networks (ANNs), within the domain of SNNs with TTFS coding.

no code implementations • 11 Nov 2023 • Amanda A Howard, Sarah H Murphy, Shady E Ahmed, Panos Stinis

The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing).

no code implementations • 28 Oct 2023 • Saad Qadeer, Andrew Engel, Amanda Howard, Adam Tsou, Max Vargas, Panos Stinis, Tony Chiang

For the regression problem of smooth functions and logistic regression classification, we show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior.

no code implementations • 27 Sep 2023 • Amit Harlev, Andrew Engel, Panos Stinis, Tony Chiang

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI.

no code implementations • 2 Sep 2023 • Wenqian Chen, Peiyuan Gao, Panos Stinis

The Ornstein-Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids.

no code implementations • 31 May 2023 • Wenqian Chen, Yucheng Fu, Panos Stinis

To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method.

1 code implementation • 8 Apr 2023 • Amanda Howard, Yucheng Fu, Panos Stinis

We introduce a novel continual learning method based on multifidelity deep neural networks.

no code implementations • 21 Mar 2023 • Wenqian Chen, Panos Stinis

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations.

no code implementations • 15 Mar 2023 • Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, George Em Karniadakis

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs).

no code implementations • 15 Mar 2023 • Shady E. Ahmed, Panos Stinis

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables.

no code implementations • 7 Feb 2023 • Panos Stinis, Constantinos Daskalakis, Paul J. Atzberger

We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems.

no code implementations • 26 Jan 2023 • Qizhi He, Mauro Perego, Amanda A. Howard, George Em Karniadakis, Panos Stinis

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise.

no code implementations • 17 Nov 2022 • Qian Zhang, Adar Kahana, George Em Karniadakis, Panos Stinis

We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs).

no code implementations • 19 Apr 2022 • Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis

We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

no code implementations • 3 Mar 2022 • Qizhi He, Yucheng Fu, Panos Stinis, Alexandre Tartakovsky

To improve the accuracy of voltage prediction at extreme ranges, we introduce a second (enhanced) DNN to mitigate the prediction errors carried from the 0D model itself and call the resulting approach enhanced PCDNN (ePCDNN).

no code implementations • 9 Nov 2021 • Brek Meuris, Saad Qadeer, Panos Stinis

In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet), to identify candidate functions on which to expand the solution of PDEs.

no code implementations • 11 Sep 2021 • Kookjin Lee, Nathaniel Trask, Panos Stinis

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees.

no code implementations • NeurIPS 2021 • Kookjin Lee, Nathaniel A. Trask, Panos Stinis

Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with reversible dynamics.

no code implementations • 21 Jun 2021 • Qizhi He, Panos Stinis, Alexandre Tartakovsky

In this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (VRFB).

no code implementations • 17 May 2019 • Panos Stinis

We present a collection of results on how to enforce constraints coming from the dynamical system in order to accelerate the training of deep neural networks to represent the flow map of the system as well as increase their predictive ability.

no code implementations • 2 Apr 2019 • Ramakrishna Tipireddy, Paris Perdikaris, Panos Stinis, Alexandre Tartakovsky

We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system.

no code implementations • 13 May 2018 • Nathan O. Hodas, Panos Stinis

We show that adding structure to the neural network that enforces higher mutual information between layers speeds training and leads to more accurate results.

no code implementations • 22 Mar 2018 • Panos Stinis, Tobias Hagge, Alexandre M. Tartakovsky, Enoch Yeung

We suggest ways to enforce given constraints in the output of a Generative Adversarial Network (GAN) generator both for interpolation and extrapolation (prediction).

no code implementations • 6 Oct 2017 • Tobias Hagge, Panos Stinis, Enoch Yeung, Alexandre M. Tartakovsky

We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term.

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