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Found 16 papers, 5 papers with code
TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework.
Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification
Unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter summarizing contribution of the embedded fibers to the overall artery stiffness.
Multi-Resolution Active Learning of Fourier Neural Operators
To overcome this problem, we propose Multi-Resolution Active learning of FNO (MRA-FNO), which can dynamically select the input functions and resolutions to lower the data cost as much as possible while optimizing the learning efficiency.
Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks
However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions.
Nonparametric Embeddings of Sparse High-Order Interaction Events
High-order interaction events are common in real-world applications.
Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs
Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers.
Weight Matrix Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures
Deep learning using neural networks is an effective technique for generating models of complex data.
Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs
We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von K\'{a}rm\'{a}n Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.
Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference
We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance.
A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world.
BIG-bench Machine Learning
Physics-informed machine learning
+1
Meta-Learning with Adjoint Methods
the initialization, we only need to run the standard ODE solver twice -- one is forward in time that evolves a long trajectory of gradient flow for the sampled task; the other is backward and solves the adjoint ODE.
Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)
Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences.
A bandit-learning approach to multifidelity approximation
Multifidelity approximation is an important technique in scientific computation and simulation.
On the computation of recurrence coefficients for univariate orthogonal polynomials
Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure.
Numerical Analysis Numerical Analysis 33D45, 42C10, 65D15
Randomized weakly admissible meshes
A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain.
Numerical Analysis Numerical Analysis Probability Computation
Analysis of The Ratio of $\ell_1$ and $\ell_2$ Norms in Compressed Sensing
We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice.
