Zhuyin Ren

Yuxuan Chen, Xu Zhu, Hua Zhou et al.

Remarkable progress has been made in automated problem solving through societies of agents based on large language models (LLMs). Computational fluid dynamics (CFD), as a complex problem, presents unique challenges in automated simulations that require sophisticated solutions. MetaOpenFOAM, as a novel multi-agent collaborations framework, aims to complete CFD simulation tasks with only natural language as input. These simulation tasks include mesh pre-processing, simulation and so on. MetaOpenFOAM harnesses the power of MetaGPT's assembly line paradigm, which assigns diverse roles to various agents, efficiently breaking down complex CFD tasks into manageable subtasks. Langchain further complements MetaOpenFOAM by integrating Retrieval-Augmented Generation (RAG) technology, which enhances the framework's ability by integrating a searchable database of OpenFOAM tutorials for LLMs. Tests on a benchmark for natural language-based CFD solver, consisting of eight CFD simulation tasks, have shown that MetaOpenFOAM achieved a high pass rate per test (85%), with each test case costing only $0.22 on average. The eight CFD simulation tasks encompass a range of multidimensional flow problems, covering compressible and incompressible flows with different physical processes. This demonstrates the capability to automate CFD simulations using only natural language input, iteratively correcting errors to achieve the desired simulations. An ablation study was conducted to verify the necessity of each component in the multi-agent system and the RAG technology. A sensitivity study on the randomness of LLM showed that LLM with low randomness can obtain more stable and accurate results. Additionally, MetaOpenFOAM owns the ability to identify and modify key parameters in user requirements, and excels in correcting bugs when failure match occur,which demonstrates the generalization of MetaOpenFOAM.

Feixue Cai, Hua Zhou, Zhuyin Ren

Calibrating chemical kinetics in a reaction-diffusion system is challenging because of complex dynamics governed by tightly coupled chemistry and transport, while experimental observations are often sparse and noisy. We propose a physics consistent diffusion-chemistry coupled neural ordinary differential equation (Diff-Chem Neural ODE) that embeds Arrhenius-structured reaction neurons into a fully differentiable streamline formulation and explicitly accounts for diffusion coupling. This design enables direct gradient-based analysis of kinetic parameters without sampling-based pretraining. We validate this method on burner-stabilized flat and stagnation reacting flows using mechanisms spanning different stiffness ranges. The proposed method reproduces species profiles with near-reference accuracy, whereas a pure chemistry Neural ODE that neglects diffusion coupling may misplace ignition and generate an incorrect thin reaction zone. Diff-Chem Neural ODE is more robust than pure chemistry Neural ODE and provides substantial speedups for gradient evaluation compared with fully discretized computations. In kinetics refinement, optimizing only a limited set of "primal" species reduces the loss by over 98% and simultaneously recovers unobserved variables, demonstrating physically consistent global control. Finally, tests with 1-20% noise in the objective show stable convergence without local overfitting, supporting its applicability under noisy measurements.

Yuxuan Chen, Xu Zhu, Hua Zhou et al.

Computational Fluid Dynamics (CFD) is widely used in aerospace, energy, and biology to model fluid flow, heat transfer, and chemical reactions. While Large Language Models (LLMs) have transformed various domains, their application in CFD remains limited, particularly for complex tasks like post-processing. To bridge this gap, we introduce MetaOpenFOAM 2.0, which leverages Chain of Thought (COT) decomposition and iterative verification to enhance accessibility for non-expert users through natural language inputs. Tested on a new benchmark covering simulation (fluid flow, heat transfer, combustion) and post-processing (extraction, visualization), MetaOpenFOAM 2.0 achieved an Executability score of 6.3/7 and a pass rate of 86.9%, significantly outperforming MetaOpenFOAM 1.0 (2.1/7, 0%). Additionally, it proved cost-efficient, averaging $0.15 per case. An ablation study confirmed that COT-driven decomposition and iterative refinement substantially improved task performance. Furthermore, scaling laws showed that increasing COT steps enhanced accuracy while raising token usage, aligning with LLM post-training scaling trends. These results highlight the transformative potential of LLMs in automating CFD workflows for industrial and research applications. Code is available at https://github.com/Terry-cyx/MetaOpenFOAM

Yuxuan Chen, Long Zhang, Xu Zhu et al.

Merging natural language interfaces with computational fluid dynamics (CFD) workflows presents transformative opportunities for both industry and research. In this study, we introduce OptMetaOpenFOAM - a novel framework that bridges MetaOpenFOAM with external analysis and optimization tool libraries through a large language model (LLM)-driven chain-of-thought (COT) methodology. By automating complex CFD tasks via natural language inputs, the framework empowers non-expert users to perform sensitivity analyses and parameter optimizations with markedly improved efficiency. The test dataset comprises 11 distinct CFD analysis or optimization tasks, including a baseline simulation task derived from an OpenFOAM tutorial covering fluid dynamics, combustion, and heat transfer. Results confirm that OptMetaOpenFOAM can accurately interpret user requirements expressed in natural language and effectively invoke external tool libraries alongside MetaOpenFOAM to complete the tasks. Furthermore, validation on a non-OpenFOAM tutorial case - namely, a hydrogen combustion chamber - demonstrates that a mere 200-character natural language input can trigger a sequence of simulation, postprocessing, analysis, and optimization tasks spanning over 2,000 lines of code. These findings underscore the transformative potential of LLM-driven COT methodologies in linking external tool for advanced analysis and optimization, positioning OptMetaOpenFOAM as an effective tool that streamlines CFD simulations and enhances their convenience and efficiency for both industrial and research applications. Code is available at https://github.com/Terry-cyx/MetaOpenFOAM.

Weiqi Ji, Zhuyin Ren, Chung K. Law

The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the uncertainty propagation in DNN. Specifically, the active subspace method is employed to identify the most important subspace in the input features using the gradient of the DNN output to the inputs. Then the response surface within that low-dimensional subspace can be efficiently built, and the uncertainty of the prediction can be acquired by evaluating the computationally cheap response surface instead of the DNN models. In addition, the subspace can help explain the adversarial examples. The approach is demonstrated in MNIST datasets with a convolutional neural network. Code is available at: https://github.com/jiweiqi/nnsubspace.