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Found 8 papers, 3 papers with code
Gaussian process learning of nonlinear dynamics
Through a Bayesian scheme, a probabilistic estimate of the model parameters is given by the posterior distribution, and thus a quantification is facilitated for uncertainties from noisy state data and the learning process.
Multi-fidelity reduced-order surrogate modeling
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given system.
Bayesian approach to Gaussian process regression with uncertain inputs
Considering two types of observables -- noise-corrupted outputs with fixed inputs and those with prior-distribution-defined uncertain inputs, a posterior distribution is estimated via a Bayesian framework to infer the uncertain data locations.
Deep Kernel Learning of Dynamical Models from High-Dimensional Noisy Data
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data.
Multi-fidelity surrogate modeling using long short-term memory networks
Especially for parametrized, time dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data.
A brief note on understanding neural networks as Gaussian processes
As a generalization of the work in [Lee et al., 2017], this note briefly discusses when the prior of a neural network output follows a Gaussian process, and how a neural-network-induced Gaussian process is formulated.
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
In this work, we present the use of artificial neural networks applied to multi-fidelity regression problems.
Energy-based error bound of physics-informed neural network solutions in elasticity
An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems.
