arXiv:2412. 00107v2 Announce Type: replace-cross Abstract: Real-time monitoring of safety-critical interior states remains an open problem in energy systems where physical instrumentation is infeasible.
arXiv:2604. 01802v2 Announce Type: replace Abstract: Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications.
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.
arXiv:2606. 00716v1 Announce Type: new Abstract: Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time.
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv:2606. 14934v1 Announce Type: cross Abstract: This work introduces the Separable Neural Architecture (SNA), a function representational class combining neural approximation with tensor decomposition.
The paper introduces Shallow Recurrent Decoder (SHRED) networks as a data‑driven method for accurate state estimation in engineering systems, specifically applied to the TRIGA Mark II research reactor. SHRED maps sparse sensor measurements to the full state space, handling noisy data and requiring minimal training time. The study demonstrates SHRED’s performance using both synthetic CFD data and experimental temperature recordings, achieving low reconstruction errors and showcasing its potential for real‑time monitoring and digital twin development.
arXiv:2512. 23292v5 Announce Type: replace Abstract: The prevailing paradigm in AI for physical systems: scaling general-purpose foundation models toward universal multimodal reasoning, confronts a barrier at the control interface.
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
The paper introduces Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
The paper introduces the Green's Observation Operator (GObO), a method that maps the ambient medium to the Green's kernel of a linear PDE restricted to source and observation submanifolds. This approach allows new sources to be evaluated with a single lower-dimensional integral, avoiding full-domain solvers and black-box surrogate evaluations. Experiments on 3‑D heat conduction and advection–diffusion show that GObO, trained on static sources, can predict moving-source responses with 4–8× lower error than black-box surrogates, achieving 1.4 ms per query after a single conditioning pass.