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Found 19 papers, 6 papers with code
Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics
This topic encompasses a broad array of methods and models aimed at solving a single or a collection of PDE problems, called multitask learning.
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra to enable efficient computation and optimization.
Neural Operator Learning for Ultrasound Tomography Inversion
Neural operator learning as a means of mapping between complex function spaces has garnered significant attention in the field of computational science and engineering (CS&E).
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
This problem is also found in, and in some sense more difficult, with domain decomposition strategies such as temporal decomposition using XPINNs.
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.
Batch Multi-Fidelity Active Learning with Budget Constraints
However, this method only queries at one pair of fidelity and input at a time, and hence has a risk to bring in strongly correlated examples to reduce 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.
Momentum Transformer: Closing the Performance Gap Between Self-attention and Its Linearization
Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence.
Adaptive Self-supervision Algorithms for Physics-informed Neural Networks
We find that training vanilla PINNs for these problems can result in up to 70% prediction error in the solution, especially in the regime of low collocation points.
Infinite-Fidelity Coregionalization for Physical Simulation
Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data.
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.
Machine Learning in Heterogeneous Porous Materials
The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials, machine learning (ML) and applied mathematics to identify how ML can advance materials research.
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
Characterizing possible failure modes in physics-informed neural networks
We provide evidence that the soft regularization in PINNs, which involves PDE-based differential operators, can introduce a number of subtle problems, including making the problem more ill-conditioned.
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.
Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks
Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions.
A bandit-learning approach to multifidelity approximation
Multifidelity approximation is an important technique in scientific computation and simulation.
Deep Multi-Fidelity Active Learning of High-dimensional Outputs
The training examples can be collected with different fidelities to allow a cost/accuracy trade-off.
Nektar++: enhancing the capability and application of high-fidelity spectral/$hp$ element methods
Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method.
Mathematical Software Numerical Analysis Numerical Analysis Fluid Dynamics
