Conformalized Physics-Informed Weak Regression for Parameter Estimation in Epidemic Models

Key points

• Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them.1
• We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty.1
• 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.1
• 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.1

Sources (1)

• [1]Conformalized Physics-Informed Weak Regression for Parameter Estimation in Epidemic Models
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 06:55 PM

  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.

  Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them.

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