Physics-informed regression gives fast accurate uncertainty for epidemic models
Conformalized Physics-Informed Weak Regression for Parameter Estimation in Epidemic Models
Machine Learning
Summary
Estimating parameters of disease spread models is important but often slow and uncertain. The authors introduce a faster and more precise method, called physics-informed weak regression, that uses the underlying math to fit parameters without needing derivative calculations and gives reliable uncertainty estimates. They also use a statistical calibration technique to produce confidence intervals that are accurate even with limited data. Their method runs quickly and outperforms or matches earlier approaches on model and real outbreak data.
What this means in practice
- •For epidemic modeling teams: Rapidly estimate disease model parameters with reliable uncertainty using data-driven but physics-based regression methods.
- •For public health data analysts: Generate calibrated confidence intervals for time-varying disease transmission rates from outbreak data efficiently and accurately.
Authors
Allan Peter Engsig-Karup
Abstract
Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them. We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty. Physics-informed regression (PIR) fits the parameters to finite-difference derivatives of the data; we introduce physics-informed weak regression (PIWR), which integrates the model in time instead, needs no derivatives of the data, estimates the initial state jointly and is high-order accurate. To quantify uncertainty we wrap both estimators in split conformal prediction, with a calibration population generated by the physics-based model itself, giving simultaneous intervals for all parameters with a finite-sample coverage guarantee. A residual-adaptive factor, computed without ground truth, scales the intervals to each data set (PIWR-RACC). On the eleven benchmark models of disease-informed neural networks (DINNs), PIWR or PIR-FD6 is one to four orders of magnitude more accurate than the reported DINN results wherever the sampling resolves the dynamics, in about a millisecond per fit instead of minutes to hours of training, and the 90% intervals achieve 87-92% coverage in all 88 settings. On the S3I3R model of the original PIR study, PIWR lowers the reported PIR errors by about three orders of magnitude. On real data from the 1978 boarding-school influenza outbreak, a variable-projection variant gives calibrated 95% intervals that overlap those of a Bayesian analysis. On a time-varying transmission benchmark, a B-spline expansion of beta(t) keeps PIR and PIWR linear; they are more accurate than physics-informed neural networks in three of four cases and comparable in the noisiest, with simultaneous bands for beta(t). The complete conformal calibration takes less than two minutes for every benchmark.