Machine Learning-Based Uncertainty Quantification in Capacity Expansion Models

System Optimization Models (ESOMs) to design cost‑effective transition pathways. Within these models, Capacity Expansion Models (CEMs) identify the optimal mix of generation, storage, and transmission infrastructure needed to meet future energy demand, while accounting for renewable integration, storage deployment, and grid expansion constraints.

Future energy systems are shaped by uncertain technological, economic, and policy developments, explicitly accounting for uncertainty is critical. However, representing uncertainty typically requires evaluating a very large number of parameter combinations, for example through Monte Carlo simulations. For large-scale systems, this approach quickly becomes computationally infeasible, as each simulation requires repeatedly solving the CEM.

To overcome this challenge, this study develops a scalable and computationally efficient surrogate model based on a Bayesian Neural Network (BNN). The surrogate is trained on a limited set of original CEM input–output data generated across defined parameter ranges. Once trained, the surrogate model can evaluate a large number of scenarios at a fraction of the computational cost, enabling practical uncertainty quantification.

The probabilistic structure of the transfer‑learning BNN (TL‑BNN) allows direct quantification of uncertainty and the computation of Sobol sensitivity indices for the model inputs. Results show that aleatoric uncertainty is highest in regions where multiple investment pathways are similarly cost‑effective. Overall, the proposed TL‑BNN framework makes uncertainty analysis computationally tractable for large‑scale energy system planning and supports efficient, robust scenario exploration.