Flora D. Salim

Jiayi Li, Zhaonan Wang, Flora D. Salim

Neural operators provide fast PDE surrogates and often generalize across parameters and resolutions. However, in the short train long test setting, autoregressive rollouts can become unstable. This typically happens for two reasons: one step errors accumulate over time, and high frequency components feed back and grow. We introduce the Spectral Generator Neural Operator (SGNO), a residual time stepper that targets both effects. For the linear part, SGNO uses an exponential time differencing update in Fourier space with a learned diagonal generator. We constrain the real part of this generator to be nonpositive, so iterating the step does not amplify the linear dynamics. For nonlinear dynamics, SGNO adds a gated forcing term with channel mixing within each Fourier mode, which keeps the nonlinear update controlled. To further limit high frequency feedback, SGNO applies spectral truncation and an optional smooth mask on the forcing pathway. We derive a one step amplification bound and a finite horizon rollout error bound. The bound separates generator approximation error from nonlinear mismatch and gives sufficient conditions under which the latent $L^2$ norm does not grow across rollout steps. On APEBench spanning 1D, 2D, and 3D PDE families, SGNO achieves lower long horizon error and longer stable rollout lengths than strong neural operator baselines. Ablations confirm the roles of the generator constraint, gating, and filtering.The code is available at https://github.com/lijy32123-cloud/SGNO.

Kirtan Bhatt, Xiachong Lin, Matthew Amos et al.

Multi-zone HVAC control is a spatial decision problem in which indoor thermal evolution and control decisions depend not only on outdoor conditions and internal heat gains but also on zone layout, physical adjacency, and delayed thermal interactions across the building. Recent LLM-based HVAC controllers have shown that prompt-based control is feasible. However, these methods typically rely on task descriptions, observation values, short textual feedback, or unstructured retrieval, which limits their ability to reason about zone coupling, thermal response, and building dynamics. This paper presents a thermodynamics-aware LLM control framework for a five-zone EnergyPlus building simulation. The controller is grounded in a physics-informed spatial knowledge graph derived from Brick-style building semantics and linked with recent interaction history. At each control step, the model receives the current building state, graph-structured spatial context, and recent environment-controller history, enabling it to make decisions that reflect both building structure and short-term thermal evolution. We evaluate the framework against standard control baselines and several LLM-based alternatives. Results show that the proposed approach achieves the best overall energy-comfort trade-off and the lowest PMV violation while maintaining energy-efficient operation.