SINDYc and MCMC for Prosumer Response Estimation

Research Question

How can we discover the governing dynamics of a prosumer (a household that both consumes and produces energy) from limited measurement data, while honestly quantifying the uncertainty in the identified model so that downstream decisions account for it?

Method

This project combined two approaches:

• SINDYc (Sparse Identification of Nonlinear Dynamics with control) — a data-driven method that selects a parsimonious dynamical model from a library of candidate basis functions, including physical terms such as differential equations and control inputs. Rather than fitting a black-box neural network, SINDYc yields an interpretable equations set that domain experts can inspect.
• MCMC (Markov-Chain Monte Carlo) — Bayesian sampling over the posterior distribution of model parameters given the data, producing calibrated uncertainty intervals rather than point estimates.

The combination produces a mechanistically grounded model — the structure comes from physical reasoning — with calibrated Bayesian uncertainty, enabling risk-aware downstream control and prediction.

The framework was implemented in Python using Stan/NUTS for posterior sampling and released as open-source software on Zenodo.

Personal Contribution

Frederik Banis was the first author and sole software developer. He developed the SINDYc-MCMC estimation framework, designed the numerical experiments, implemented the software, and wrote the manuscript. Co-authors contributed supervision, methodological guidance, and review.

Validation and Key Results

• The SINDYc-identified model captured prosumer response dynamics with interpretable terms rather than opaque coefficients.
• MCMC posterior intervals provided calibrated uncertainty bands on parameter estimates, distinguishing well-identified parameters from uncertain ones.
• The approach demonstrated that sparse identification combined with Bayesian inference produces models suitable for downstream decision-making under uncertainty.

The method was published in Energies (2020), a peer-reviewed open-access journal.

Outputs

• Journal paper: DOI 10.3390/en13123183
• Open-source software: SINDYc and MCMC Framework (Zenodo, v1.1.1)
• PhD thesis: Efficient Operation of Energy Grids, DTU, 2020. DOI 10.11581/DTU.00000334

Collaborators

• DTU Compute, Technical University of Denmark — Henrik Madsen, Niels Kjølstad Poulsen (supervisors)
• Daniela Guericke (co-author)

Status and Next Steps

Status: Published (2020). The software is archived on Zenodo for reproducibility; it is no longer actively maintained (historical).

Transfer to current research: The core idea — combining mechanistic structure identification with Bayesian uncertainty quantification — is the same methodological base that now underpins uncertainty-aware inference for adaptive biomedical sensing. The shift is from energy-system dynamics to physiological signal models, but the inferential architecture is shared.

See the Software catalogue for detailed metadata on the SINDYc and MCMC Framework, and the Methods page for the methodological context.