Autoregressive PDE foundation models enable fast full-field forecasting but accumulate errors as predicted states are recursively reused. We introduce Event-Triggered Context Healing (ETCH), which compares forecasts with measurements from 12 cylinder-surface pressure taps. When their discrepancy exceeds a threshold, pressure-conditioned hourglass diffusion transformers reconstruct the velocity--pressure context for subsequent predictions. On 43 RealPDEBench Cylinder trajectories, ETCH reduces velocity and pressure errors from 48.05 and 63.71% to 6.29 and 7.25% for DPOT, and from 74.97 and 76.91% to 5.16 and 6.84% for Poseidon-T, using the same reconstructors and threshold. For DPOT, correcting 14.56% of windows maintains errors close to reconstructing every window and supports average real-time forecasting and correction on an A100 GPU. These results show that sparse physical feedback stabilizes long autoregressive rollouts across PDE foundation models while reducing reconstruction cost.

Real-time monitoring of safety-critical interior states remains an open problem across energy, environmental, and industrial systems where direct instrumentation is infeasible. Existing approaches based on governing equations, discrete state vectors, or fixed sensor locations fail to provide mesh-independent, field-level reconstructions at arbitrary interior coordinates under real-time constraints. Here we introduce neural operator-based virtual sensing as a general framework for recovering inaccessible interior fields from sparse, heterogeneous measurements and operating conditions, instantiated with MIMONet, a multi-input, multi-output neural operator that fuses heterogeneous inputs and decodes coupled physical fields through a shared latent representation. Across three engineering-grade evaluations of escalating complexity, from confined recirculating flows to pressurized water reactor subchannels and compact power-system heat exchangers, MIMONet achieves ≤5% relative reconstruction error, while generating full-field predictions with sub-millisecond inference on an NVIDIA H200, at least five orders of magnitude faster than traditional high-fidelity CFD simulations, with calibrated uncertainty and noise resilience demonstrated on the heat-exchanger case. We validate the framework on three independent real-world datasets spanning electrochemical energy, atmospheric science, and physical oceanography: current-density mapping in a hydrogen fuel cell, wind-speed profiling on instrumented meteorological towers, and North Atlantic ocean-state from a global ocean reanalysis. MIMONet improves over classical virtual-sensing baselines by 72–84%: 84% on fuel-cell internal-field recovery from 10% sensor coverage and 83% on hub-height wind-speed recovery from lower-level tower sensors. Most notably, it recovers sea-surface height, a field with zero direct sensors, from its learned coupling to observed temperature and salinity at 4.1 × lower error than the best classical predictor, a cross-modal field recovery beyond the reach of classical interpolation. These results establish operator-based virtual sensing as a practical route to real-time field observability in systems where the states that matter most cannot be directly measured.

Deep neural operators learn mappings between input functions and complete PDE solution fields, enabling forward evaluations of new problem instances orders of magnitude faster than conventional numerical solvers. Attention mechanisms have recently been introduced into neural operators, but most studies change several architectural components at once, making it difficult to identify what actually improves accuracy. This work presents a controlled and systematic study of five deep operator network (DeepONet) variants with distinct attention mechanisms, trained under both data-driven and physics-informed regimes, to isolate the effects of cross-attention, self-attention, tokenization, and attention depth. We evaluate them on a source-driven transient one-dimensional nonlinear diffusion-reaction equation, a transient one-dimensional viscous Burgers equation with variable initial conditions, and a two-dimensional Poisson heat-conduction problem with heterogeneous source fields. Per-sensor tokenization with cross-attention reduces the mean relative L_2 error of the classical DeepONet in all benchmark-training combinations by factors of 2.4-28.0, while the best attention configurations reach 3.5-32.3. Branch self-attention paired only with dot-product fusion is inconsistent, degrading the one-dimensional problems while helping the more complex two-dimensional source field; added on top of cross-attention it improves all six cases, though by less than cross-attention fusion alone. Global pre-mixing provides no consistent benefit. Increasing cross-attention depth further improves accuracy, but with diminishing returns and a substantially higher cost under physics-informed training. Overall, query-dependent cross-attention is the most reliable mechanism, whereas branch self-attention is most useful for large, spatially complex functional inputs.

Real-time prediction of complex physical systems requires surrogate models that learn from data while representing strong multiphysics coupling. Deep Operator Networks have shown success in single-physics problems, yet their effectiveness in capturing nonlinear interactions in coupled systems (such as thermo-mechanical or electro-thermal coupling) remains underexplored. Here we pose a practical question: should the architecture of a neural operator reflect the strength of physical coupling it aims to model? We compare single-branch and multi-branch designs, in both feedforward and sequential recurrent forms, across three representative systems: a reaction-diffusion problem with heterogeneous sources, a nonlinear thermo-electrical problem with temperature-dependent conductivity and Joule heating, and a viscoplastic thermo-mechanical model of steel solidification. Single-branch networks consistently outperform multi-branch variants in tightly coupled regimes by encouraging shared latent representations, whereas multi-branch designs remain favorable for decoupled or single-physics tasks. Once trained, these surrogates deliver full-field predictions up to 1.8 × 104 times faster than physics-based solvers.

The prevailing paradigm in AI for physical systems: scaling general-purpose foundation models toward universal multimodal reasoning, confronts a barrier at the control interface. Frontier vision–language models achieve only 50–53% accuracy on basic quantitative physics tasks, behaving as approximate guessers that preserve semantic plausibility while violating physical constraints. Safety-critical control demands outcome-space guarantees over executed actions, not parameter-space imitation. Here, we present what is, to our knowledge, the first demonstration of Agentic Physical AI for nuclear reactor control: a domain-specific foundation model in which a compact language model learns control policies through physics-based simulator validation rather than perceptual inference. The framework unifies three capabilities: Agentic AI generates and selects among admissible control strategies; Physical AI evaluates those strategies through closed-loop execution in a reactor simulator; and a domain-specific foundation model acquires reusable control priors through data scaling. Under nominal simulated conditions, scaling yields regime-dependent gains in reliability, including an approximately 500-fold reduction in outcome variance and elimination of terminal-power excursions above 10% on the sampled distribution. Although trained with balanced exposure to four actuation families, the model concentrates 95% of runtime execution on a single-bank strategy without reinforcement learning or reward engineering. The learning framework transfers across reactor simulators without architectural redesign. These results establish a pathway toward reusable, physics-validated foundation-model intelligence for safety-critical control.

Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in engineering design evaluation, a wide range of neural operator architectures have been proposed for various problem settings. However, model selection remains challenging due to the absence of fair and comprehensive comparisons. To address this, we propose and standardize six representative 3D industry-scale engineering design datasets spanning thermal analysis, linear elasticity, elasto-plasticity, time-dependent plastic problems, and computational fluid dynamics. All datasets include fully preprocessed inputs and outputs for model training, making them directly usable across diverse neural operator architectures. Using these datasets, we conduct a systematic comparison of four types of neural operator variants, including Branch-Trunk-based Neural Operators inspired by DeepONet, Graph-based Neural Operators inspired by Graph Neural Networks, Grid-based Neural Operators inspired by Fourier Neural Operators, and Point-based Neural Operators inspired by PointNet. We further introduce practical enhancements to adapt these models to different engineering settings, improving the fairness of the comparison. Our benchmarking study evaluates each model strengths and limitations in terms of predictive performance, computational efficiency, memory usage, and deployment complexity. The findings provide actionable insights to guide future neural operator development.