Positivity-Preserving Neural Surrogates for Reduced-Precision Inference of a Dynamic-Energy-Budget Angiogenesis Model

Neural surrogates of evolution equations replace many solver steps by one network evaluation, but the physical invariants they appear to respect are properties of the trained weights, and weights are what reduced-precision and integer inference perturb. We study a six-field reaction, diffusion and taxis model of angiogenesis coupled to a Dynamic Energy Budget reserve, whose fields are densities and must stay nonnegative, and we build a macro-step surrogate whose forward pass factors through operators with known sign structure. The diffusion propagator is assembled once as a dense nonnegative row-stochastic matrix, the haptotaxis step is written with explicitly nonnegative coefficients, and the learned block returns a production and a per capita destruction that enter a Modified–Patankar quotient. Every operation is then a sum or a product of nonnegative numbers, or a quotient of a nonnegative number by a positive one, so the state stays nonnegative under any arithmetic whose rounding preserves the sign of nonnegative reals. Positivity survives half precision, bfloat16 and integer quantization without clamping and without retraining, which we confirm against an unstructured surrogate sharing the backbone, the parameter count and the training protocol. Measurements on a graphics processor quantify what each format costs in accuracy, time and memory.