Project case study · Scientific machine learning

Disease-Informed Neural Networks for Epidemic Mobility Models

A controlled experiment in which synthetic observations and the governing epidemic equations train the same neural network.

Ongoing scientific-machine-learning projectPhase 1 implementedSynthetic-data experiment

Problem

Can a neural network learn an epidemic trajectory without ignoring the model that produced it?

Why it matters

A standard data fit can reproduce observations while behaving poorly between them or violating known dynamics. This project adds the differential equations to the training objective, so the learned curves must answer to both data and model structure.

Phase 1 result

A synthetic SIRD trajectory, learned under equation constraints.

The horizontal axis is time in days. The vertical axis is the fraction of the modeled population in each state. S is susceptible, I is infected, R is recovered, and D is deceased.

S SusceptibleI InfectedR RecoveredD Deceased

Solid synthetic SIRD trajectories and dashed disease-informed neural-network trajectories plotted over 160 days — Synthetic-data experiment. Solid lines are the known trajectories used to generate the controlled data; dashed lines are the neural-network fit.Reading the figure. The curves overlap closely in this experiment. This shows trajectory recovery under the current synthetic setup; it does not show forecasting skill or real-outbreak validation.

Method

Five signals shape the learning problem.

Synthetic observations

Numerically generated SIRD values provide controlled data points for the four state trajectories.

Data-fit loss

Penalizes differences between the neural-network output and the synthetic observations.

Initial-condition loss

Anchors the learned trajectory at the known state of the system at the start of the experiment.

Differential-equation residual loss

Uses automatic differentiation to measure how closely the network output satisfies the SIRD equations through time.

Trainable epidemic parameters

Treats selected model parameters as quantities to be recovered jointly with the state trajectories.

My contribution

Connecting the mathematical model to the training objective.

I implemented the current PyTorch phase, expressed the SIRD residuals through automatic differentiation, and structured the loss so trajectory fit, initial conditions, and governing equations could be assessed together. I am now developing the broader workflow.

Evaluation design

A setting where the reference answer is known.

Because the observations are synthetic, the learned trajectories can be compared directly with the numerical solution that generated them. That is useful for checking the method before any move toward more complex models.

Interpretation

Promising as a controlled recovery experiment—still early as an epidemic application.

The current figure shows that the network can reproduce the synthetic SIRD trajectory under the implemented loss. On the same synthetic experiment, the learned transmission, recovery, and mortality parameters were 0.5000, 0.2000, and 0.0715, compared with generating values of 0.5000, 0.2000, and 0.0714. Each relative error was below 0.1%.

Those results belong to a controlled synthetic setting. This version does not make claims about real-outbreak estimation, forecasting, deployment, or uncertainty.

Planned extensions

Movement enters next—not retroactively.

These directions are part of the project plan, not current results.

Planned

Two-region movement model

Extend the controlled framework to connected regions so movement parameters and coupled dynamics can be studied explicitly.

Planned

Multipatch SIS model

Bring the scientific-machine-learning experiment closer to the patch-based SIS questions at the center of my doctoral research.

Repository & status

Follow the implemented phase in the public repository.

View code and project notes