Generative Robust Optimisation

Classical uncertainty sets for robust optimisation impose fixed geometric shapes that cannot represent the complex dependencies present in real-world data. We propose Generative Robust Optimisation (GRO), a framework in which a deep generative model defines the uncertainty set as the image of a neural network decoder over a calibrated latent set, naturally accommodating nonlinear correlations, asymmetry, and multimodality. A five-point evaluation framework (reconstruction fidelity, distribution matching, latent regularity, robust relevance, and computational tractability) provides systematic, model-agnostic criteria for assessing any neural network-based uncertainty set. We instantiate this framework with a Wasserstein Adversarial Autoencoder employing Gaussian mixture model-guided training for latent regularity and constraint-consistency regularisation for robust relevance. Restricting the decoder to ReLU activations enables exact worst-case verification through mixed-integer programming embedding. Extensive experiments on a production planning problem across six uncertainty distributions and six generative architectures, together with a multi-period facility location study, validate the framework and demonstrate that systematic attention to all five criteria yields uncertainty sets that are simultaneously expressive, well-calibrated, and optimisation-tractable.

Powering the Future of AI: Navigating the Trade-offs for Europe's Energy Transition and Net-Zero Goals

The rapid expansion of AI globally has led to the proliferation of energy-intensive hyperscale data centres (DCs), making them as a structurally challenging component in power system planning and operation. Using a spatially explicit optimisation model of Europe across 21 AI growth scenarios, we systematically quantify additional demand, capacity requirements, emissions, and operational impacts of DCs. Results indicate that AI could drive 73-723 TWh of extra demand by 2050, risking cumulative emissions overshoots of 67-181 MtCO2 between 2030 and 2050. Our analysis indicates that after 2030, the geography of AI infrastructure will be shaped more by firm power and system flexibility than by the mere abundance of clean energy. In moderate scenarios, AI requires an additional of 200 hours of firm generation, which increases LCOE by 35 EUR/MWh in key hubs. We show that even under the pessimistic scenarios, existing infrastructure would require 70 GW additional capacity, while under managed growth pathways, this expansion could reach 226 GW. We further find DCs workload dynamics strongly shape energy dispatch, system flexibility, and emissions, while improved efficiency significantly reduces capacity needs, and system peaks. While our findings suggest that net-zero targets for 2050 may be achieved, critical emission risks may appear in the intermediate years, and the EU may compromise its carbon-neutral goals unless policies adapt to this accelerating digital transformation.