Table 1 Listing of all data-driven models explored in the manuscript.
From: Data-driven discovery of chemotactic migration of bacteria via coordinate-invariant machine learning
Model | Surrogate function | Known fields | Known RHSs | Output | Algorithm |
|---|---|---|---|---|---|
Black box for 2 PDEs | \(f_{GP}, h_{GP}\) | b(r, t), c(r, t) | – | \(b_t, c_t\) | GPR |
\(f_{NN}, h_{NN}\) | b(r, t), c(r, t) | – | \(b_t, c_t\) | ANN | |
Black box for 1 PDE | \(f_{GP}\) | b(r, t), c(r, t) | \(c_t\) | \(b_t\) | GPR |
\(f_{NN}\) | b(r, t), c(r, t) | \(c_t\) | \(b_t\) | ANN | |
Black box, delays | \(f^{partial}_{GP}\) | b(r, t), history | – | \(b(r, t+\Delta t)\) | GPR |
\(f^{partial}_{NN}\) | b(r, t), history | – | \(b(r, t+\Delta t)\) | ANN | |
Gray box | \(g_{GP}\) | b(r, t), c(r, t) | \(c_t\) | \(b_t-D_b\Delta b\) | GPR |
\(g_{NN}\) | b(r, t), c(r, t) | \(c_t\) | \(b_t-D_b\Delta b\) | ANN | |
Gray box, delays | \(g^{partial}_{GP}\) | b(r, t), history | – | \(b(r, t+\Delta t)-D_b\Delta b(r,t)\) | GPR |
\(g^{partial}_{NN}\) | b(r, t), history | – | \(b(r, t+\Delta t)-D_b\Delta b(r,t)\) | ANN |