Probabilistic Numerics for an ODE-Constrained Battery Model
Overview
What this challenge is about.
You receive 12 months of charge/discharge cycle data for 50 battery packs from a delivery-van fleet, plus the existing single-particle ODE degradation model (Python). Use a probabilistic ODE solver (e.g., ProbNum) plus NumPyro / Stan to fit posteriors over the 5 ODE parameters per pack. Run hierarchical inference so packs share information across the fleet. Validate posterior calibration on the most recent month per pack (predictive coverage of the 80 percent interval). Success is interval coverage between 75 and 85 percent and a 2-page note on what the parameter posteriors imply for fleet remaining-useful-life forecasting.
The Brief
What you'll do, and what you'll demonstrate.
Replace a deterministic ODE-fit with a probabilistic-numerics-based hierarchical Bayesian fit that produces calibrated joint posteriors over parameters and trajectories.
Earning criteria — what you'll demonstrate
- Integrate probabilistic ODE solvers into a Bayesian-inference workflow
- Build hierarchical priors that share information across related units
- Validate posterior calibration via predictive coverage on held-out data
- Communicate uncertainty in physics-based ML to a non-academic audience
Program Fit
Where this fits in your program.
Sharpens the same skills your degree expects you to demonstrate.
Skills
Skills you'll demonstrate.
Each one shows up on your verified credential.
Careers
Roles this prepares you for.
Real titles. Real skill bridges. Pick the one closest to your trajectory.
Career paths this builds toward
Canonical rolesResearch Scientist
Integrating probabilistic numerics with hierarchical Bayesian inference on a real engineering problem is portfolio-grade work for industrial research scientist roles.
This challenge sharpens
- probabilistic-numerics
- hierarchical-models
- ode-modeling
Applied AI Scientist
Translating Bayesian posteriors into a fleet-facing RUL story is exactly the work applied AI scientists do at industrial-AI startups.
This challenge sharpens
- bayesian-inference
- uncertainty-quantification
- ode-modeling
ML Researcher
Choosing solver priors, justifying pooling structure, and reporting calibration are the rigor signals ML research teams look for.
This challenge sharpens
- probabilistic-numerics
- bayesian-inference
- hierarchical-models