3-D Representations for Hyperspectral Flame Tomography

Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.

GLU: Global-Local-Uncertainty Fusion for Scalable Spatiotemporal Reconstruction and Forecasting

Digital twins of complex physical systems are expected to infer unobserved states from sparse measurements and predict their evolution in time, yet these two functions are typically treated as separate tasks. Here we present GLU, a Global-Local-Uncertainty framework that formulates sparse reconstruction and dynamic forecasting as a unified state-representation problem and introduces a structured latent assembly to both tasks. The central idea is to build a structured latent state that combines a global summary of system-level organization, local tokens anchored to available measurements, and an uncertainty-driven importance field that weights observations according to the physical informativeness. For reconstruction, GLU uses importance-aware adaptive neighborhood selection to retrieve locally relevant information while preserving global consistency and allowing flexible query resolution on arbitrary geometries. Across a suite of challenging benchmarks, GLU consistently improves reconstruction fidelity over reduced-order, convolutional, neural operator, and attention-based baselines, better preserving multi-scale structures. For forecasting, a hierarchical Leader-Follower Dynamics module evolves the latent state with substantially reduced memory growth, maintains stable rollout behavior and delays error accumulation in nonlinear dynamics. On a realistic turbulent combustion dataset, it further preserves not only sharp fronts and broadband structures in multiple physical fields, but also their cross-channel thermo-chemical couplings. Scalability tests show that these gains are achieved with substantially lower memory growth than comparable attention-based baselines. Together, these results establish GLU as a flexible and computationally practical paradigm for sparse digital twins.

Latent Generative Solvers for Generalizable Long-Term Physics Simulation

We study long-horizon surrogate simulation across heterogeneous PDE systems. We introduce Latent Generative Solvers (LGS), a two-stage framework that (i) maps diverse PDE states into a shared latent physics space with a pretrained VAE, and (ii) learns probabilistic latent dynamics with a Transformer trained by flow matching. Our key mechanism is an uncertainty knob that perturbs latent inputs during training and inference, teaching the solver to correct off-manifold rollout drift and stabilizing autoregressive prediction. We further use flow forcing to update a system descriptor (context) from model-generated trajectories, aligning train/test conditioning and improving long-term stability. We pretrain on a curated corpus of $\sim$2.5M trajectories at $128^2$ resolution spanning 12 PDE families. LGS matches strong deterministic neural-operator baselines on short horizons while substantially reducing rollout drift on long horizons. Learning in latent space plus efficient architectural choices yields up to \textbf{70$\times$} lower FLOPs than non-generative baselines, enabling scalable pretraining. We also show efficient adaptation to an out-of-distribution $256^2$ Kolmogorov flow dataset under limited finetuning budgets. Overall, LGS provides a practical route toward generalizable, uncertainty-aware neural PDE solvers that are more reliable for long-term forecasting and downstream scientific workflows.