# Intelligent Optimization of Multi-Parameter Micromixers Using a Scientific Machine Learning Framework

arXiv: https://arxiv.org/abs/2511.07702 · HTML: https://mlsanity.com/paper/2511.07702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations](https://mlsanity.com/paper/2005.05092/) (2020)
- [Physics-informed neural networks for solving parametric magnetostatic problems](https://mlsanity.com/paper/2202.04041/) (2022)

## Abstract (arXiv)

Multidimensional optimization has consistently been a critical challenge in engineering. However, traditional simulation-based optimization methods have long been plagued by significant limitations: they are typically capable of optimizing only a single problem at a time and require substantial computational time for meshing and numerical simulation. This paper introduces a novel framework leveraging cutting-edge Scientific Machine Learning (Sci-ML) methodologies to overcome these inherent drawbacks of conventional approaches. The proposed method provides instantaneous solutions to a spectrum of complex, multidimensional optimization problems. A micromixer case study is employed to demonstrate this methodology. An agent, operating on a Deep Reinforcement Learning (DRL) architecture, serves as the optimizer to explore the relationships between key problem parameters. This optimizer interacts with an environment constituted by a parametric Physics-Informed Neural Network (PINN), which responds to the agent's actions at a significantly higher speed than traditional numerical methods. The agent's objective, conditioned on the Schmidt number is to discover the optimal geometric and physical parameters that maximize the micromixer's efficiency. After training the agent across a wide range of Schmidt numbers, we analyzed the resulting optimal designs. Across this entire spectrum, the achieved efficiency was consistently greater than the baseline, normalized value. The maximum efficiency occurred at a Schmidt number of 13.3, demonstrating an improvement of approximately 32%. Finally, a comparative analysis with a Genetic Algorithm was conducted under equivalent conditions to underscore the advantages of the proposed method.