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 parameter-distribution estimation.

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, retaining uncertainty over plausible parameter values rather than only a point estimate.

The combination produces a sparse, interpretable model with posterior parameter distributions. The paper studies a synthetic two-prosumer example; it does not validate the method on measured household data or in a downstream controller.

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.
• Experiments with five and fifty input sequences showed how the amount of excitation affects identification.
• Some posterior means approached the generating parameter values, while some posterior distributions remained displaced from the true distributions.
• The posterior predictive check was described as suboptimal. Application in stochastic MPC was identified as future work rather than demonstrated.

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 sparse structure identification with posterior inference and explicit model checking — informs uncertainty-aware inference for adaptive biomedical sensing. The application has shifted from synthetic energy-system dynamics to physiological signals.

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