Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading

Most PDE foundation models are pretrained and fine-tuned on fluid-centric benchmarks. Their utility under extreme-loading material dynamics remains unclear. We benchmark out-of-distribution transfer on two discontinuity-dominated regimes in which shocks, evolving interfaces, and fracture produce highly non-smooth fields: shock-driven multi-material interface dynamics (perturbed layered interface or PLI) and dynamic fracture/failure evolution (FRAC). We formulate the downstream task as terminal-state prediction, i.e., learning a long-horizon map that predicts the final state directly from the first snapshot without intermediate supervision. Using a unified training and evaluation protocol, we evaluate two open-source pretrained PDE foundation models, POSEIDON and MORPH, and compare fine-tuning from pretrained weights against training from scratch across training-set sizes to quantify sample efficiency under distribution shift.

PDE foundation model-accelerated inverse estimation of system parameters in inertial confinement fusion

PDE foundation models are typically pretrained on large, diverse corpora of PDE datasets and can be adapted to new settings with limited task-specific data. However, most downstream evaluations focus on forward problems, such as autoregressive rollout prediction. In this work, we study an inverse problem in inertial confinement fusion (ICF): estimating system parameters (inputs) from multi-modal, snapshot-style observations (outputs). Using the open JAG benchmark, which provides hyperspectral X-ray images and scalar observables per simulation, we finetune the PDE foundation model and train a lightweight task-specific head to jointly reconstruct hyperspectral images and regress system parameters. The fine-tuned model achieves accurate hyperspectral reconstruction (test MSE 1.2e-3) and strong parameter-estimation performance (up to R^2=0.995). Data-scaling experiments (5%-100% of the training set) show consistent improvements in both reconstruction and regression losses as the amount of training data increases, with the largest marginal gains in the low-data regime. Finally, finetuning from pretrained MORPH weights outperforms training the same architecture from scratch, demonstrating that foundation-model initialization improves sample efficiency for data-limited inverse problems in ICF.

Advancing accelerator virtual beam diagnostics through latent evolution modeling: an integrated solution to forward, inverse, tuning, and UQ problems

Virtual beam diagnostics relies on computationally intensive beam dynamics simulations where high-dimensional charged particle beams evolve through the accelerator. We propose Latent Evolution Model (LEM), a hybrid machine learning framework with an autoencoder that projects high-dimensional phase spaces into lower-dimensional representations, coupled with transformers to learn temporal dynamics in the latent space. This approach provides a common foundational framework addressing multiple interconnected challenges in beam diagnostics. For \textit{forward modeling}, a Conditional Variational Autoencoder (CVAE) encodes 15 unique projections of the 6D phase space into a latent representation, while a transformer predicts downstream latent states from upstream inputs. For \textit{inverse problems}, we address two distinct challenges: (a) predicting upstream phase spaces from downstream observations by utilizing the same CVAE architecture with transformers trained on reversed temporal sequences along with aleatoric uncertainty quantification, and (b) estimating RF settings from the latent space of the trained LEM using a dedicated dense neural network that maps latent representations to RF parameters. For \textit{tuning problems}, we leverage the trained LEM and RF estimator within a Bayesian optimization framework to determine optimal RF settings that minimize beam loss. This paper summarizes our recent efforts and demonstrates how this unified approach effectively addresses these traditionally separate challenges.

Adaptive conditional latent diffusion maps beam loss to 2D phase space projections

Beam loss (BLM) and beam current monitors (BCM) are ubiquitous at particle accelerator around the world. These simple devices provide non-invasive high level beam measurements, but give no insight into the detailed 6D (x,y,z,px,py,pz) beam phase space distributions or dynamics. We show that generative conditional latent diffusion models can learn intricate patterns to map waveforms of tens of BLMs or BCMs along an accelerator to detailed 2D projections of a charged particle beam's 6D phase space density. This transformational method can be used at any particle accelerator to transform simple non-invasive devices into detailed beam phase space diagnostics. We demonstrate this concept via multi-particle simulations of the high intensity beam in the kilometer-long LANSCE linear proton accelerator.

Physics-Informed Super-Resolution Diffusion for 6D Phase Space Diagnostics

Adaptive physics-informed super-resolution diffusion is developed for non-invasive virtual diagnostics of the 6D phase space density of charged particle beams. An adaptive variational autoencoder (VAE) embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a 326 pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent 2D projections. Physics-guided super-resolution diffusion transforms low-resolution images of the 6D density to high resolution 256x256 pixel images. Un-supervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multi-particle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without re-training.

CBOL-Tuner: Classifier-pruned Bayesian optimization to explore temporally structured latent spaces for particle accelerator tuning

Complex dynamical systems, such as particle accelerators, often require complicated and time-consuming tuning procedures for optimal performance. It may also be required that these procedures estimate the optimal system parameters, which govern the dynamics of a spatiotemporal beam -- this can be a high-dimensional optimization problem. To address this, we propose a Classifier-pruned Bayesian Optimization-based Latent space Tuner (CBOL-Tuner), a framework for efficient exploration within a temporally-structured latent space. The CBOL-Tuner integrates a convolutional variational autoencoder (CVAE) for latent space representation, a long short-term memory (LSTM) network for temporal dynamics, a dense neural network (DNN) for parameter estimation, and a classifier-pruned Bayesian optimizer (C-BO) to adaptively search and filter the latent space for optimal solutions. CBOL-Tuner demonstrates superior performance in identifying multiple optimal settings and outperforms alternative global optimization methods.

Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal

Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally expensive, limiting their utility for solving inverse problems online. The problem of estimating upstream six-dimensional phase space given downstream measurements of charged particles in an accelerator is an inverse problem of growing importance. This paper introduces a reverse Latent Evolution Model (rLEM) designed for temporal inversion of forward beam dynamics. In this two-step self-supervised deep learning framework, we utilize a Conditional Variational Autoencoder (CVAE) to project 6D phase space projections of a charged particle beam into a lower-dimensional latent distribution. Subsequently, we autoregressively learn the inverse temporal dynamics in the latent space using a Long Short-Term Memory (LSTM) network. The coupled CVAE-LSTM framework can predict 6D phase space projections across all upstream accelerating sections based on single or multiple downstream phase space measurements as inputs. The proposed model also captures the aleatoric uncertainty of the high-dimensional input data within the latent space. This uncertainty, which reflects potential uncertain measurements at a given module, is propagated through the LSTM to estimate uncertainty bounds for all upstream predictions, demonstrating the robustness of the LSTM against in-distribution variations in the input data.

A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding simulations, and inherent uncertainties in the system. We propose a two-step unsupervised deep learning framework named as Conditional Latent Autoregressive Recurrent Model (CLARM) for learning the spatiotemporal dynamics of charged particles in accelerators. CLARM consists of a Conditional Variational Autoencoder (CVAE) transforming six-dimensional phase space into a lower-dimensional latent distribution and a Long Short-Term Memory (LSTM) network capturing temporal dynamics in an autoregressive manner. The CLARM can generate projections at various accelerator modules by sampling and decoding the latent space representation. The model also forecasts future states (downstream locations) of charged particles from past states (upstream locations). The results demonstrate that the generative and forecasting ability of the proposed approach is promising when tested against a variety of evaluation metrics.

Physics-constrained 3D Convolutional Neural Networks for Electrodynamics

We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t) from which we generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt. Our PCNNs satisfy hard constraints, such as div(B)=0, by construction. Soft constraints push A and V towards satisfying the Lorenz gauge.

Artificial Intelligence and Machine Learning in Nuclear Physics

Advances in artificial intelligence/machine learning methods provide tools that have broad applicability in scientific research. These techniques are being applied across the diversity of nuclear physics research topics, leading to advances that will facilitate scientific discoveries and societal applications. This Review gives a snapshot of nuclear physics research which has been transformed by artificial intelligence and machine learning techniques.