• Multi-fidelity Neural Network

Multi-fidelity neural network (MFNN) is used for modeling physical systems by multi-fidelity data. In real applications, low-fidelity data is usually abundant but less accurate, and high-fidelity data is scarce and expensive. MFNN makes uses of both low- and high-fidelity data for modeling the physical system, which significantly improves data accuracy by a small set of high-fidelity data.

Meng and Karniadakis [1] gave an approach to MFNN by using a composite neural network. However, the code is absent for their paper. Meanwhile, the use of liner layers in high-fidelity DNN (NN_H1) is redundant, as linear features will always be modeled by the nonlinear DNN (NN_H2).

Thus, in this repository, a modified version of MFNN is provided, where linear DNN (NN_H1) given by paper [1] are replaced by residual connection over the nonlinear DNN (NN_H2).The code is implemented using pytorch, and examples are provided for MFNN.

• Snapshots

** Data

[[./snapshots/data.svg]]

** Modeling using low-fidelity data

[[./snapshots/low.svg]]

** Modeling by high-fidelity data

[[./snapshots/high.svg]]

** Modeling by both low- and high-fidelity data

[[./snapshots/mfnn.svg]]

• References [1] Meng X, Karniadakis GE. A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. Journal of Computational Physics 2020;401:109020. https://doi.org/10.1016/j.jcp.2019.109020.