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To address the pervasive failure of neural networks to extrapolate outside their training domain, this work evaluates physics-guided architectures—specifically PINNs and BiLSTMs—on a 1D transient diffusion benchmark with a known analytical ground truth. The benchmark rigorously tests out-of-distribution generalization by requiring models trained on intermediate regimes to extrapolate forward toward steady-state and backward toward an initial mathematical singularity. By coupling physics-guided coordinate transforms and boundary-aware learning with an iterative temporal marching scheme, the framework achieves stable, physically consistent predictions well beyond the initial training horizon.
Extrapolating neural networks backward toward sharp mathematical singularities—historically a fatal failure mode for scientific ML—becomes reliable when physics-guided coordinate transforms are coupled with recursive prediction-extension loops.
Machine learning models used in engineering are typically trained within limited operating ranges, yet reliable predictions are often required beyond these domains. Consequently, the primary challenge is extrapolation rather than interpolation. Rigorous validation is hindered by the scarcity of data outside the training range. To address this limitation, a novel extrapolation framework is integrated with established machine learning architectures to enable accurate and physically consistent predictions beyond the training domain. The framework is established by systematically evaluating two physics-guided architectures: a Bidirectional Long Short-Term Memory (BiLSTM) network and a Physics-Informed Neural Network (PINN). A classical one-dimensional transient diffusion problem is adopted as a benchmark because its exact analytical solution provides unlimited, reliable data across the spatio-temporal domain, enabling rigorous quantitative validation. The problem is particularly challenging because the solution evolves from an initial singularity through a strongly nonlinear transient regime before approaching a steady-state linear profile. When training data are confined to an intermediate portion of this evolution, backward extrapolation toward the singularity becomes especially demanding. To improve reliability, physics-guided coordinate transformations, boundary-aware learning strategies, and stability-enhancing temporal marching are incorporated. Extrapolation is evaluated using a train-predict-validate-extend strategy, in which validated predictions are recursively added to the training set to progressively extend the prediction horizon. The results demonstrate accurate and physically consistent predictions beyond the training domain, highlighting the framework's potential for engineering applications where data availability is limited.