Biomimetic causal learning for microstructure-forming phase transitions

Nonconvex multi-well energies in cell-induced phase transitions give rise to fine-scale microstructures, low-regularity transition layers and sharp interfaces, all of which pose numerical challenges for physics-informed learning. To address this, we propose biomimetic physics-informed neural networks (Bio-PINNs) for cell-induced phase transitions in fibrous extracellular matrices. The method converts the outward progression of cell-mediated remodelling into a distance-based training curriculum and couples it to uncertainty-driven collocation that concentrates samples near evolving interfaces and tether-forming regions. The same uncertainty proxy provides a lower-cost alternative to explicit second-derivative regularization. We also establish structural guarantees for the adaptive sampler, including persistent coverage under gate expansion and quantitative near-to-far accumulation. Across single- and multi-cell benchmarks, diverse separations, and various regularization regimes, Bio-PINNs consistently recover sharp transition layers and tether morphologies, significantly outperforming state-of-the-art adaptive and ungated baselines.

Biomimetic PINNs for Cell-Induced Phase Transitions: UQ-R3 Sampling with Causal Gating

Nonconvex multi-well energies in cell-induced phase transitions give rise to sharp interfaces, fine-scale microstructures, and distance-dependent inter-cell coupling, all of which pose significant challenges for physics-informed learning. Existing methods often suffer from over-smoothing in near-field patterns. To address this, we propose biomimetic physics-informed neural networks (Bio-PINNs), a variational framework that encodes temporal causality into explicit spatial causality via a progressive distance gate. Furthermore, Bio-PINNs leverage a deformation-uncertainty proxy for the interfacial length scale to target microstructure-prone regions, providing a computationally efficient alternative to explicit second-derivative regularization. We provide theoretical guarantees for the resulting uncertainty-driven ``retain-resample-release" adaptive collocation strategy, which ensures persistent coverage under gating and establishing a quantitative near-to-far growth bound. Across single- and multi-cell benchmarks, diverse separations, and various regularization regimes, Bio-PINNs consistently recover sharp transition layers and tether morphologies, significantly outperforming state-of-the-art adaptive and ungated baselines.