The Multiphysics Object-Oriented Simulation Environment (MOOSE) is an open-source finite-element framework for building multiphysics simulation applications. Using a multiphysics environment effectively demands specialized expertise, creating a barrier for many domain scientists and engineers. MOOSEnger, developed at Idaho National Laboratory (INL), is a domain-specific, tool-enabled AI agent built for the MOOSE Framework. This work extends MOOSEnger with a harness focused on locally-hosted models. The harness gives the agent a full pipeline: it retrieves contextual knowledge from the MOOSE repository, validates and diagnoses the resulting input through interaction with the simulation executable environment, and extracts and stores lessons in a persistent memory. The resulting framework is demonstrated on an engineering problem from the National Reactor Innovation Center Virtual Test Bed (VTB), illustrating its potential to support realistic multiphysics simulation workflows. Additionally, the agent performance is evaluated on different categories including diffusion, Navier--Stokes, phase field, plasticity, porous media flow, solid mechanics, transient heat transfer, and reactor mesh generation. Each category consists of 25 prompts/cases. We compare MOOSEnger-Gemma4 against MOOSEnger-GPT-5.2, alongside baseline Gemma4 and GPT-5.2 without agentic capabilities. MOOSEnger-GPT-5.2 shows a slight edge, achieving a 90\% success rate versus 76.5\% for MOOSEnger-Gemma4. The baseline models perform far worse, at just 5\% (GPT-5.2) and 0\% (Gemma4), underscoring the impact of the agentic harness.
Multiphysics simulation is critical for system-technology co-optimization (STCO) in chiplet-based design, but repeated finite-element solutions of PDE-governed problems are computationally expensive in parametric design exploration. This paper proposes a variational matrix-learning Fourier network (VMLFN) for efficient parametric multiphysics surrogate modeling. VMLFN constructs a log-space sine neural representation with randomly sampled spectral frequencies, frequency-dependent decay regulation, and embedded Dirichlet boundary conditions. With fixed hidden-layer parameters, the output-layer weights are determined by reformulating the governing PDEs into variational weak forms and enforcing the stationarity condition of the resulting energy functional. This converts physics-informed training into a linear matrix-solving problem, requiring only first-order derivatives and avoiding both high-order automatic differentiation and penalty-coefficient tuning. A heuristic frequency-scanning algorithm is further introduced to select a problem-adaptive maximum frequency that covers the dominant spectral range of the target problem. The proposed method is validated on heat conduction, solid mechanics, and Helmholtz wave propagation problems. Results from five benchmark cases demonstrate that VMLFN delivers accurate full-field predictions with substantial speedup over conventional physics-informed neural networks and repeated finite-element simulations.