Milad Kazemi

Hannah Lydon, Milad Kazemi, Martin Bishop et al.

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to discretisation, while canonical deep learning methods are data-hungry and struggle with chaotic dynamics and long-term predictions. Physics-Informed Neural Networks (PINNs) mitigate some of these issues by incorporating physical constraints in the learning process, yet they remain limited by mesh resolution and long-term predictive stability. In this work, we propose a Physics-Informed Neural Operator (PINO) approach to solve PDE problems in cardiac EP. Unlike PINNs, PINO models learn mappings between function spaces, allowing them to generalise to multiple mesh resolutions and initial conditions. Our results show that PINO models can accurately reproduce cardiac EP dynamics over extended time horizons and across multiple propagation scenarios, including zero-shot evaluations on scenarios unseen during training. Additionally, our PINO models maintain high predictive quality in long roll-outs (where predictions are recursively fed back as inputs), and can scale their predictive resolution by up to 10x the training resolution. These advantages come with a significant reduction in simulation time compared to numerical PDE solvers, highlighting the potential of PINO-based approaches for efficient and scalable cardiac EP simulations.

Tom Kuipers, Renukanandan Tumu, Shuo Yang et al.

Off-Policy Prediction (OPP), i.e., predicting the outcomes of a target policy using only data collected under a nominal (behavioural) policy, is a paramount problem in data-driven analysis of safety-critical systems where the deployment of a new policy may be unsafe. To achieve dependable off-policy predictions, recent work on Conformal Off-Policy Prediction (COPP) leverage the conformal prediction framework to derive prediction regions with probabilistic guarantees under the target process. Existing COPP methods can account for the distribution shifts induced by policy switching, but are limited to single-agent systems and scalar outcomes (e.g., rewards). In this work, we introduce MA-COPP, the first conformal prediction method to solve OPP problems involving multi-agent systems, deriving joint prediction regions for all agents' trajectories when one or more ego agents change their policies. Unlike the single-agent scenario, this setting introduces higher complexity as the distribution shifts affect predictions for all agents, not just the ego agents, and the prediction task involves full multi-dimensional trajectories, not just reward values. A key contribution of MA-COPP is to avoid enumeration or exhaustive search of the output space of agent trajectories, which is instead required by existing COPP methods to construct the prediction region. We achieve this by showing that an over-approximation of the true joint prediction region (JPR) can be constructed, without enumeration, from the maximum density ratio of the JPR trajectories. We evaluate the effectiveness of MA-COPP in multi-agent systems from the PettingZoo library and the F1TENTH autonomous racing environment, achieving nominal coverage in higher dimensions and various shift settings.