Periodicity-Enforced Neural Network for Designing Deterministic Lateral Displacement Devices
Andrew Lee, Mahir Mobarrat, Xiaolin Chen
TL;DR
This work tackles the high computational cost of CFD-based DLD device design by introducing a periodicity-enforced surrogate that predicts full flow fields ($u$, $v$, $p$) for unit cells and guarantees exact boundary matching across repeated units. It achieves this through a periodic transformation in the input layer and three dedicated sub-networks, enabling accurate critical diameter predictions ($D_c$) with an average validation error of $0.478\%$, while maintaining perfect periodicity. The method surpasses baseline models by enforcing architectural periodicity rather than penalty-based imposition, trading a modest increase in single-unit $D_c$ error for robust multi-unit stability and flow-field fidelity. The framework provides a complete flow-field representation to enable gradient-based optimization and post-hoc analyses, with significant practical impact for rapid, reliable DLD device design in cancer diagnostics. Future directions include integrating Navier–Stokes residuals for label-free training and extending geometric generalization to broader post shapes, viscosities, and Reynolds-number regimes.
Abstract
Deterministic Lateral Displacement (DLD) devices enable liquid biopsy for cancer detection by separating circulating tumor cells (CTCs) from blood samples based on size, but designing these microfluidic devices requires computationally expensive Navier-Stokes simulations and particle-tracing analyses. While recent surrogate modeling approaches using deep learning have accelerated this process, they often inadequately handle the critical periodic boundary conditions of DLD unit cells, leading to cumulative errors in multi-unit device predictions. This paper introduces a periodicity-enforced surrogate modeling approach that incorporates periodic layers, neural network components that guarantee exact periodicity without penalty terms or output modifications, into deep learning architectures for DLD device design. The proposed method employs three sub-networks to predict steady-state, non-dimensional velocity and pressure fields (u, v, p) rather than directly predicting critical diameters or particle trajectories, enabling complete flow field characterization and enhanced design flexibility. Periodic layers ensure exact matching of flow variables across unit cell boundaries through architectural enforcement rather than soft penalty-based approaches. Validation on 120 CFD-generated geometries demonstrates that the periodic layer implementation achieves 0.478% critical diameter error while maintaining perfect periodicity consistency, representing an 85.4% improvement over baseline methods. The approach enables efficient and accurate DLD device design with guaranteed boundary condition satisfaction for multi-unit device applications.