Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations
Read the original on arXiv Machine Learning →The paper introduces a Physics‑Informed Method of Group Data Handling (PI‑GMDH) that builds functional representations of coupled physical fields progressively during the solution process, rather than fixing the structure beforehand. Using tensor‑product Chebyshev functions, the method is applied to the incompressible Navier‑Stokes equations in a two‑dimensional time‑dependent Taylor‑Green benchmark, achieving extremely low validation and test losses with a modest number of active functions. Comparative experiments with degree‑by‑degree, all‑terms PI‑GMDH, and reference PINN/KAN configurations demonstrate that selective progressive construction can yield a favorable balance of accuracy, model size, and computational time for this controlled synthetic benchmark.
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