Neural PDEs offer efficient alternatives to computationally expensive numerical PDE solvers for simulating complex physical systems. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we are able to quantify and calibrate the model's inconsistencies with the PDE rather than the uncertainty arising from the data. Our approach uses convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

We propose a method for obtaining statistically guaranteed confidence bands for functional machine learning techniques: surrogate models which map between function spaces, motivated by the need build reliable PDE emulators. The method constructs nested confidence sets on a low-dimensional representation (an SVD) of the surrogate model's prediction error, and then maps these sets to the prediction space using set-propagation techniques. The result are conformal-like coverage guaranteed prediction sets for functional surrogate models. We use zonotopes as basis of the set construction, due to their well studied set-propagation and verification properties. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also elicit a technique to capture the truncation error of the SVD, ensuring the guarantees of the method.

Neural weather models have shown immense potential as inexpensive and accurate alternatives to physics-based models. However, most models trained to perform weather forecasting do not quantify the uncertainty associated with their forecasts. This limits the trust in the model and the usefulness of the forecasts. In this work we construct and formalise a conformal prediction framework as a post-processing method for estimating this uncertainty. The method is model-agnostic and gives calibrated error bounds for all variables, lead times and spatial locations. No modifications are required to the model and the computational cost is negligible compared to model training. We demonstrate the usefulness of the conformal prediction framework on a limited area neural weather model for the Nordic region. We further explore the advantages of the framework for deterministic and probabilistic models.

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (MSE $\approx$ $10^{-5}$). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations (PDE), and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e., cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

Nuclear fusion using magnetic confinement holds promise as a viable method for sustainable energy. However, most fusion devices have been experimental and as we move towards energy reactors, we are entering into a new paradigm of engineering. Curating a design for a fusion reactor is a high-dimensional multi-output optimisation process. Through this work we demonstrate a proof-of-concept of an AI-driven strategy to help explore the design search space and identify optimum parameters. By utilising a Multi-Output Bayesian Optimisation scheme, our strategy is capable of identifying the Pareto front associated with the optimisation of the toroidal field coil shape of a tokamak. The optimisation helps to identify design parameters that would minimise the costs incurred while maximising the plasma stability by way of minimising magnetic ripples.

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required temporal dependencies. However, most existing sequential models operate within finite-dimensional Euclidean spaces which offer limited functionality when employed in modelling physics relevant data. Alternatively recent work with neural operator learning within the Fourier space has shown efficient strategies for parameterising Partial Differential Equations (PDE). In this work, we propose a novel sequential model, built to handle Physics relevant data by way of amalgamating the conventional RNN architecture with that of the Fourier Neural Operators (FNO). The Fourier-RNN allows for learning the mappings from the input to the output as well as to the hidden state within the Fourier space associated with the temporal data. While the Fourier-RNN performs identical to the FNO when handling PDE data, it outperforms the FNO and the conventional RNN when deployed in modelling noisy, non-Markovian data.