arXiv subjects

Mengnan Li

Publications and source records attributed to Mengnan Li.

7 recordsLinked to original sources

arXiv2026

Deploying Frontier Agentic Technology in MOOSEnger, a Multiphysics-Capable AI Assistant

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.

cs.LG↗

arXiv2026

Decoupling scales via localized subspace iteration and temporal splitting for multiscale parabolic equations

Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the Localized Subspace Iteration (LSI) framework to multiscale parabolic equations. The proposed method constructs optimal, low-dimensional trial spaces by iteratively approximating the dominant eigenspaces of local inverse operators via Localized Standard Subspace Iteration (LSSI) or Localized Krylov Subspace Iteration (LKSI). Because these LSI basis functions are inherently tailored to capture the slow-decaying, low-frequency modes of the parabolic solution, they naturally suppress error accumulation over long-term integration. To further improve computational efficiency, we decouple the basis construction into an offline phase and implement a contrast-independent, partially explicit temporal splitting scheme for online time-stepping. By explicitly advancing the dominant macroscopic modes while implicitly treating high-frequency microscopic corrections, this scheme guarantees stability without imposing restrictive time-step constraints. We establish rigorous a priori error estimates in both the energy and $L^2$ norms. Numerical experiments illustrate the accuracy and efficiency of the LSI framework, particularly highlighting the LKSI method's advantages in handling high-contrast, complex multiscale media.

math.NA↗

arXiv2026

MOOSEnger -- a Domain-Specific AI Agent for the MOOSE Ecosystem

MOOSEnger is a tool-enabled AI agent tailored to the Multiphysics Object-Oriented Simulation Environment (MOOSE). MOOSE cases are specified in HIT ".i" input files; the large object catalog and strict syntax make initial setup and debugging slow. MOOSEnger offers a conversational workflow that turns natural-language intent into runnable inputs by combining retrieval-augmented generation over curated docs/examples with deterministic, MOOSE-aware parsing, validation, and execution tools. A core-plus-domain architecture separates reusable agent infrastructure (configuration, registries, tool dispatch, retrieval services, persistence, and evaluation) from a MOOSE plugin that adds HIT-based parsing, syntax-preserving ingestion of input files, and domain-specific utilities for input repair and checking. An input precheck pipeline removes hidden formatting artifacts, fixes malformed HIT structure with a bounded grammar-constrained loop, and resolves invalid object types via similarity search over an application syntax registry. Inputs are then validated and optionally smoke-tested with the MOOSE runtime in the loop via an MCP-backed execution backend (with local fallback), translating solver diagnostics into iterative verify-and-correct updates. Built-in evaluation reports RAG metrics (faithfulness, relevancy, context precision/recall) and end-to-end success by actual execution. On a 125-prompt benchmark spanning diffusion, transient heat conduction, solid mechanics, porous flow, incompressible Navier--Stokes, phase field and plasticity, MOOSEnger achieves a 0.90 execution pass rate versus 0.06 for an LLM-only baseline.

cs.AI↗

arXiv2023

Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media

In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators. Different from the case of autonomous dynamical systems, the Koopman operator family of nonautonomous dynamical systems significantly depend on a time pair. In order to effectively estimate the time-dependent Koopman operators, a moving time window is used to decompose the snapshot data, and the extended dynamic mode decomposition method is applied to computing the Koopman operators in each local temporal domain. Many physical properties in multiscale media often vary in very different scales. In order to capture multiscale information well, the dimension of collected data may be high. To accurately construct the models of dynamical systems in multiscale media, we use high spatial dimension of observation data. It is challenging to compute the Koopman operators using the very high dimensional data. Thus, the strategy of reduced-order modeling is proposed to treat the difficulty. The proposed reduced-order modeling includes two stages: offline stage and online stage. In offline stage, a block-wise low rank decomposition is used to reduce the spatial dimension of initial snapshot data. For the nonautonomous dynamical systems, real-time observation data may be required to update the Koopman operators. The online reduced-order modeling is proposed to correct the offline reduced-order modeling. Three methods are developed for the online reduced-order modeling: fully online, semi-online and adaptive online. The adaptive online method automatically selects the fully online or semi-online and can achieve a good trade-off between modeling accuracy and efficiency.

math.NA↗

arXiv2022

Online multiscale model reduction for nonlinear stochastic PDEs with multiplicative noise

In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation nonlinearly depends on the diffusion dynamics. It is necessary to efficiently compute all possible trajectories of the stochastic dynamics for quantifying model's uncertainty and statistic moments. The multiscale diffusion and nonlinearity may cause the computation intractable. To overcome the multiscale difficulty, a constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) is used to localize the computation and obtain an effective coarse model. However, the nonlinear terms are still defined on a fine scale space after the Galerkin projection of CEM-GMsFEM is applied to the nonlinear SPDEs. This significantly impacts on the simulation efficiency by CEM-GMsFEM. To this end, a stochastic online discrete empirical interpolation method (DEIM) is proposed to treat the stochastic nonlinearity. The stochastic online DEIM incorporates offline snapshots and online snapshots. The offline snapshots consist of the nonlinear terms at the approximate mean of the stochastic dynamics and are used to construct an offline reduced model. The online snapshots contain some information of the current new trajectory and are used to correct the offline reduced model in an increment manner. The stochastic online DEIM substantially reduces the dimension of the nonlinear dynamics and enhances the prediction accuracy for the reduced model. Thus, the online multiscale model reduction is constructed by using CEM-GMsFEM and the stochastic online DEIM. A priori error analysis is carried out for the nonlinear SPDEs. We present a few numerical examples with diffusion in heterogeneous porous media and show the effectiveness of the proposed model reduction.

math.NA↗

arXiv2020

Nucleate Boiling Simulation using Interface Tracking Method

The development and validation of 3D multiphase computational fluid dynamics (M-CFD) models and physics-informed data-driven modeling require data of high-quality and high-resolution. Considering the difficulties in acquiring the corresponding experimental data in prototypical conditions, two-phase boiling simulations by Interface Tracking Method (ITM) based models can be used to generate high-resolution numerical data in a consistent and relatively economical manner. A boiling model is developed in one of the ITM-based multiphase-flow solvers, named PHASTA, to investigate the nucleate boiling phenomenon. The interaction between bubbles forming at adjacent nucleation sites is investigated with this ITM boiling model. Nucleate pool boiling simulations with multiple nucleation sites are presented in this paper and influences of site distance, neighboring bubble size and contact angle effect are investigated. The presented boiling model can conduct boiling simulation on 3D unstructured computational meshes. These simulation results improve our understanding of the physical mechanisms of the nucleate boiling phenomenon and provide high-resolution numerical data for M-CFD validation and advanced boiling model development.

physics.flu-dyn↗

arXiv2018

A Constraint energy minimizing generalized multiscale finite element method for parabolic equations

In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the construction of CEM-GMsFEM and rigorously analyze its convergence for the parabolic equations. The convergence rate is characterized by the coarse grid size and the eigenvalue decay of local spectral problems, but is independent of the scale length and contrast of the media. The analysis shows that the method has a first order convergence rate with respect to coarse grid size in the energy norm and second order convergence rate with respect to coarse grid size in $L^2$ norm under some appropriate assumptions. For the temporal discretization, finite difference techniques are used and the convergence analysis of full discrete scheme is given. Moreover, a posteriori error estimator is derived and analyzed. A few numerical results for porous media applications are presented to confirm the theoretical findings and demonstrate the performance of the approach.

math.NA↗