Magnetic confinement fusion may one day provide reliable, carbon-free energy, but the field currently faces technical hurdles. In this position paper, we highlight six key research challenges in the field of fusion energy that we believe should be research priorities for the Machine Learning (ML) community because they are especially ripe for ML applications: (1) disruption prediction, (2) simulation and dynamics modeling (3) resolving partially observed data, (4) improving controls, (5) guiding experiments with optimal design, and (6) enhancing materials discovery. For each problem, we give background, review past ML work, suggest features of future models, and list challenges and idiosyncrasies facing ML development. We also discuss ongoing efforts to update the fusion data ecosystem and identify opportunities further down the line that will be enabled as fusion and its data infrastructure advance. It is our position that fusion energy offers especially exciting opportunities for ML practitioners to impact decarbonization and the future of energy.

This study introduces a novel transformer model optimized for large-scale point cloud processing in scientific domains such as high-energy physics (HEP) and astrophysics. Addressing the limitations of graph neural networks and standard transformers, our model integrates local inductive bias and achieves near-linear complexity with hardware-friendly regular operations. One contribution of this work is the quantitative analysis of the error-complexity tradeoff of various sparsification techniques for building efficient transformers. Our findings highlight the superiority of using locality-sensitive hashing (LSH), especially OR & AND-construction LSH, in kernel approximation for large-scale point cloud data with local inductive bias. Based on this finding, we propose LSH-based Efficient Point Transformer (**HEPT**), which combines E$^2$LSH with OR & AND constructions and is built upon regular computations. HEPT demonstrates remarkable performance on two critical yet time-consuming HEP tasks, significantly outperforming existing GNNs and transformers in accuracy and computational speed, marking a significant advancement in geometric deep learning and large-scale scientific data processing. Our code is available at https://github.com/Graph-COM/HEPT.

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Raynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known “failure modes”.

This paper explores challenges in training Physics-Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in minimizing the PINN loss function, particularly due to ill-conditioning caused by differential operators in the residual term. We compare gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-BFGS, showing the superiority of Adam+L-BFGS, and introduce a novel second-order optimizer, NysNewton-CG (NNCG), which significantly improves PINN performance. Theoretically, our work elucidates the connection between ill-conditioned differential operators and ill-conditioning in the PINN loss and shows the benefits of combining first- and second-order optimization methods. Our work presents valuable insights and more powerful optimization strategies for training PINNs, which could improve the utility of PINNs for solving difficult partial differential equations.