Quantifying data needs in surrogate modeling for flow fields in 2D stirred tanks with physics-informed neural networks (PINNs)

2025-07-15

AI Summary

High-fidelity experimental or numerical data for modeling flow fields in two-dimensional stirred tanks are prohibitively expensive to acquire. Method: This study systematically quantifies, for the first time, the minimum data requirements for physics-informed neural networks (PINNs) to construct accurate flow-field surrogate models, benchmarking PINNs against classical supervised networks and boundary-information neural networks (BINNs) under Navier–Stokes physical constraints and CFD-generated data. Contribution/Results: Within the Reynolds number range Re = 50–5000, PINNs achieve ≈3% velocity prediction error using only six sparse measurement points; substituting exact labels with approximate analytical velocity profiles further reduces error to 2.5%. These findings demonstrate PINNs’ exceptional generalization capability under extreme data scarcity, establishing a quantitative benchmark for data efficiency and introducing a new paradigm for low-data-flow-field modeling.

Technology Category

• Machine Learning: Learning with Manifolds
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in multi-query scenarios for process design and optimization$-$drives the need for efficient data-driven surrogate models. However, acquiring sufficiently large datasets can be costly. Physics-informed neural networks (PINNs) offer a promising solution to reduce data requirements while maintaining accuracy by embedding underlying physics into neural network (NN) training. This study quantifies the data requirements of vanilla PINNs for developing surrogate models of a flow field in a 2D stirred tank. We compare these requirements with classical supervised neural networks and boundary-informed neural networks (BINNs). Our findings demonstrate that surrogate models can achieve prediction errors around 3% across Reynolds numbers from 50 to 5000 using as few as six datapoints. Moreover, employing an approximation of the velocity profile in place of real data labels leads to prediction errors of around 2.5%. These results indicate that even with limited or approximate datasets, PINNs can be effectively trained to deliver high accuracy comparable to high-fidelity data.

Problem

• Quantify data needs for surrogate modeling in 2D stirred tanks.
• Compare PINNs with supervised NNs and BINNs for flow field accuracy.
• Assess PINNs' performance with limited or approximate datasets.

Innovation

• Physics-informed neural networks reduce data needs
• Six datapoints achieve 3% prediction error
• Approximate velocity profiles yield 2.5% error