Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems

By Liang Yan, Ling Guo. 2015

32 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. G. Em Karniadakis
2. Paris Perdikaris
3. Guofei Pang
4. Lu Lu
5. Maizar Raissi
6. Wei Cai
7. Liu Yang
8. Yibo Yang

In Statistics and Probability

1. G. Em Karniadakis
2. Paris Perdikaris
3. Lu Lu
4. Guofei Pang
5. Wei Cai
6. Dongbin Xiu
7. Nicholas Zabaras
8. Anthony Nouy

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “The first category exploits only the information of observed data in the spatio-temporal domain, and employs surrogate models such as Gaussian process regression (GP regression) [16], stochastic collocation methods [17], and feedforward neural networks (NNs) [18, 19] to approximate the mapping from ”
• Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization (2017, methodology): “System input x ∈ Rd x ∈ Rd System output f (x) ∈ R1 G(x) ∈ Rn Observation/data y(x) = ||G(x)−C0 || ||C0 || = f (x) + C0 = G(x) + η Prior fN ∼ N (m,K)(∈ RN ) x ∼ P(m0, 0) Likelihood p(yN |fN ) = p( N ),yN , N ∈ RN p(C0|G(x)) = p(η), z,η ∈ Rn Posterior p(fN |yN ) p(x|C0) Optimal input xopt = arg minx{”