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Found 13 papers, 2 papers with code
Mathematical Opportunities in Digital Twins (MATH-DT)
It illustrates that foundational Mathematical advances are required for Digital Twins (DTs) that are different from traditional approaches.
On-Manifold Projected Gradient Descent
We use these tools to obtain adversarial examples that reside on a class manifold, yet fool a classifier.
GNEP Based Dynamic Segmentation and Motion Estimation for Neuromorphic Imaging
This paper explores the application of event-based cameras in the domains of image segmentation and motion estimation.
A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Method
Again, these networks can be trained in parallel, for each EIM point.
Neural Network Representation of Time Integrators
Deep neural network (DNN) architectures are constructed that are the exact equivalent of explicit Runge-Kutta schemes for numerical time integration.
An Optimal Time Variable Learning Framework for Deep Neural Networks
The proposed framework can be applied to any of the existing networks such as ResNet, DenseNet or Fractional-DNN.
NINNs: Nudging Induced Neural Networks
The NINNs framework can be applied to almost all pre-existing DNNs, with forward propagation, with costs comparable to existing DNNs.
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments.
Novel Deep neural networks for solving Bayesian statistical inverse
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs).
Fractional Deep Neural Network via Constrained Optimization
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one another.
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization.
Adaptive particle-based approximations of the Gibbs posterior for inverse problems
To manage the computational cost of propagating increasing numbers of particles through the loss function, we employ a recently developed local reduced basis method to build an efficient surrogate loss function that is used in the Gibbs update formula in place of the true loss.
A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications
While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute.
Distributed, Parallel, and Cluster Computing General Relativity and Quantum Cosmology Numerical Analysis
