Plasma Surrogate Modelling using Fourier Neural Operators

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.

Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach

We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.

Evaluating Self-Supervised Learning for Molecular Graph Embeddings

Graph Self-Supervised Learning (GSSL) paves the way for learning graph embeddings without expert annotation, which is particularly impactful for molecular graphs since the number of possible molecules is enormous and labels are expensive to obtain. However, by design, GSSL methods are not trained to perform well on one downstream task but aim for transferability to many, making evaluating them less straightforward. As a step toward obtaining profiles of molecular graph embeddings with diverse and interpretable attributes, we introduce Molecular Graph Representation Evaluation (MolGraphEval), a suite of probe tasks, categorised into (i) topological-, (ii) substructure-, and (iii) embedding space properties. By benchmarking existing GSSL methods on both existing downstream datasets and MolGraphEval, we discover surprising discrepancies between conclusions drawn from existing datasets alone versus more fine-grained probing, suggesting that current evaluation protocols do not provide the whole picture. Our modular, automated end-to-end GSSL pipeline code will be released upon acceptance, including standardised graph loading, experiment management, and embedding evaluation.

Stochastic Causal Programming for Bounding Treatment Effects

Causal effect estimation is important for numerous tasks in the natural and social sciences. However, identifying effects is impossible from observational data without making strong, often untestable assumptions. We consider algorithms for the partial identification problem, bounding treatment effects from multivariate, continuous treatments over multiple possible causal models when unmeasured confounding makes identification impossible. We consider a framework where observable evidence is matched to the implications of constraints encoded in a causal model by norm-based criteria. This generalizes classical approaches based purely on generative models. Casting causal effects as objective functions in a constrained optimization problem, we combine flexible learning algorithms with Monte Carlo methods to implement a family of solutions under the name of stochastic causal programming. In particular, we present ways by which such constrained optimization problems can be parameterized without likelihood functions for the causal or the observed data model, reducing the computational and statistical complexity of the task.