TOFLUX: A Differentiable Topology Optimization Framework for Multiphysics Fluidic Problems

2025-08-24

AI Summary

Topology optimization (TO) holds significant promise for fluid device design, yet its practical application is severely hindered by the challenges of modeling and differentiating strongly coupled, nonlinear multiphysics systems. Conventional manual differentiation is error-prone and inefficient, while existing automatic differentiation (AD) approaches have not been effectively extended to complex fluid TO scenarios. This paper introduces, for the first time, a JAX-based differentiable programming framework for multiphysics fluid TO, enabling end-to-end differentiable modeling of tightly coupled systems—including thermal–fluid, fluid–structure, and non-Newtonian flow interactions. By unifying forward simulation and gradient-based optimization within a single computational graph, our approach achieves high-fidelity, efficient sensitivity computation and natively supports integration with neural networks and machine learning techniques. An open-source implementation lowers methodological barriers, fostering open innovation and rapid iteration in fluid TO research.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Topology Optimization (TO) holds the promise of designing next-generation compact and efficient fluidic devices. However, the inherent complexity of fluid-based TO systems, characterized by multiphysics nonlinear interactions, poses substantial barriers to entry for researchers. Beyond the inherent intricacies of forward simulation models, design optimization is further complicated by the difficulty of computing sensitivities, i.e., gradients. Manual derivation and implementation of sensitivities are often laborious and prone to errors, particularly for non-trivial objectives, constraints, and material models. An alternative solution is automatic differentiation (AD). Although AD has been previously demonstrated for simpler TO problems, extending its use to complex nonlinear multiphysics systems, specifically in fluidic optimization, is key to reducing the entry barrier. To this end, we introduce TOFLUX, a TO framework for fluid devices leveraging the JAX library for high-performance automatic differentiation. The flexibility afforded by AD enables the rapid exploration and evaluation of various objectives and constraints. We illustrate this capability through challenging examples encompassing thermo-fluidic coupling, fluid-structure interaction, and non-Newtonian flows. Additionally, we demonstrate the seamless integration of our framework with neural networks and machine learning methodologies, enabling modern approaches to scientific computing. Ultimately, the framework aims to provide a foundational resource to accelerate research and innovation in fluid-based TO. The software accompanying this educational paper can be accessed at github.com/UW-ERSL/TOFLUX.

Problem

• Automates sensitivity computation for fluid topology optimization
• Reduces barriers in multiphysics nonlinear fluidic system design
• Enables gradient-based optimization through automatic differentiation

Innovation

• Leverages JAX library for automatic differentiation
• Enables rapid exploration of objectives and constraints
• Integrates with neural networks and machine learning