Prosumer Response Estimation Using SINDYc in Conjunction with Markov-Chain Monte-Carlo Sampling

Problem and Research Question

Prosumers — households that both consume and produce energy (e.g., via rooftop solar) — exhibit complex dynamics that are difficult to model from first principles. Understanding how prosumers respond to price signals, weather, and control inputs is essential for demand-side management in smart grids. The central question: how can we discover the governing dynamics of a prosumer from limited measurement data, while honestly quantifying the uncertainty in the identified model so that downstream decisions account for it?

Black-box machine learning models can fit the data but do not yield interpretable equations. Pure physical modeling requires detailed system knowledge that is often unavailable. The gap is a method that combines physical structure with data-driven identification and calibrated uncertainty.

Method

This paper combined two complementary 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 set of equations that domain experts can inspect and validate.
• 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. This allows downstream controllers to account for parameter uncertainty in their decisions.

The combination produces a mechanistically grounded model — the structure comes from physical reasoning via the SINDYc library — 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 (10.5281/zenodo.3911952).

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 Henrik Madsen, Niels Kjølstad Poulsen, and Daniela Guericke 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, producing equations that domain experts can inspect.
• 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 — not just point predictions, but risk-aware ones.

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

Related Outputs

• Open-source software: SINDYc and MCMC Framework (Zenodo, v1.1.1) — Python and Stan/NUTS implementation
• PhD thesis: Efficient Operation of Energy Grids, DTU, 2020. DOI: 10.11581/DTU.00000334

Collaborators and Institutions

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

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 related project page for the broader research context, the Software catalogue for software metadata, and the Methods page for the methodological framework.