Allan Peter Engsig‐Karup

Parameter estimation for epidemic compartment models no longer needs neural-network training. Physics-informed regression previously estimated time derivatives from data, and that derivative estimate became the accuracy bottleneck when sampling was coarse or noise large, while point estimates carried no uncertainty. The new physics-informed weak regression integrates the model in time instead, keeps the equations linear in the parameters, estimates the unknown initial state jointly, and reaches fourth-order accuracy with cubic-spline quadrature; across the eleven DINN benchmarks it is the most accurate estimator in 15 of 22 model/noise settings, one to four orders of magnitude more accurate than the reported DINN results where sampling resolves the dynamics, at about a millisecond per fit.

Parameter estimation for epidemic compartment models no longer needs neural-network training. Physics-informed regression previously estimated time derivatives from data, and that derivative estimate became the accuracy bottleneck when sampling was coarse or noise large, while point estimates carried no uncertainty. The new physics-informed weak regression integrates the model in time instead, keeps the equations linear in the parameters, estimates the unknown initial state jointly, and reaches fourth-order accuracy with cubic-spline quadrature; across the eleven DINN benchmarks it is the most accurate estimator in 15 of 22 model/noise settings, one to four orders of magnitude more accurate than the reported DINN results where sampling resolves the dynamics, at about a millisecond per fit.