Unsteady Cylinder Wakes from Arbitrary Bodies with Differentiable Physics-Assisted Neural Network (2308.04296v2)

Abstract: This work delineates a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

• The paper introduces a hybrid DPNN that combines a differentiable flow solver with neural networks to enhance unsteady fluid flow modeling.
• It demonstrates lower mean absolute errors and preserves both global wake dynamics and near-wall boundary layers across up to 100 unique cylinder configurations.
• The framework paves the way for future advancements in chaotic flow prediction and improved computational efficiency in complex fluid dynamics simulations.

Analysis of Hybrid Predictive Models for Unsteady Fluid Dynamics Using Differentiable Physics-Assisted Neural Networks

The paper "Unsteady Cylinder Wakes from Arbitrary Bodies with Differentiable Physics-Assisted Neural Network" by Shuvayan Brahmachary and Nils Thuerey introduces a differentiated physics-assisted neural network (DPNN) as a hybrid surrogate model for unsteady fluid flows around arbitrary cylindrical configurations. These flows present complex dynamics due to variations in geometry and arrangement. The authors propose a method integrating a base differentiable flow solver, PhiFlow, with a neural network, leveraging the differentiability of both components to establish end-to-end recurrent training. This enables the framework to optimize predictive accuracy in reconstructing fluid flow fields over extended temporal horizons.

Summary of Approach

The primary objective is to predictively model wake flows behind multiple cylinders of arbitrary shapes. Such flows are characterized by a variety of wake behaviors, including periodic, chaotic, and other complex transitions influenced by the geometric configuration of the cylinders. Fueling this approach is the combination of a differentiable solver with neural networks to enable nuanced corrections to the computational solvability of flow fields. The neural architecture is trained to address inaccuracies in base solvers which typically suffer from issues like inadequate boundary condition representation. The team's conceptualization of the problem leverages a well-structured segmented neural framework, using ResNets and other convolutional-based architectures favorably tailored to fluid dynamics.

Quantitative Outcomes

A significant portion of the analysis is dedicated to benchmarking predictive models against known literature values and computational setups. The paper reports testing using a dataset with up to 100 unique configurations, where the DPNN consistently produced lower mean absolute errors, demonstrating superior long-term prediction accuracy over the supervised learning (SL) and base solver-only approaches. Quantitatively, the DPNN effectively preserved both global wake dynamics and finer-scale near-wall boundary layers, manifesting as low kinetic energy decay and consistent Strouhal numbers with known experimental data.

Implications and Forward-Looking Statements

The research holds promise for advancing surrogate modeling in fluid dynamics by establishing frameworks that accommodate large dynamic ranges and interact with computational fluid dynamics solvers. Its implications extend into both engineering applications requiring flow predictions around complex structures and potential cross-domain machine learning advancements, given the demonstrated efficiency in multi-scale predictions. By highlighting robust corrective capabilities, the framework suggests future progress may include refining chaotic flow predictions further and improving computational resource efficiency via potentially reduced solver invocation.

Furthermore, the paper underscores areas for future inquiry, such as the explicit exploration of generalization performance on complex real-world geometries and the enhancement of neural solvers to manage more turbulent flow regimes beyond the tested Reynolds numbers. As more intricate physical models demand increased precision and predictive reliability, the incorporation of higher-dimensional temporal-spatial datasets will likely augment model robustness.

Conclusion

This paper expands the frontier of fluid dynamics modeling through the innovative assembly of differentiable physics in machine learning frameworks, setting a compelling precedent for future developments in physics-informed predictive analytics. While current challenges like chaotic prediction stability and solver generalization persist, the adaptability of the DPNN framework offers expansive opportunities for tackling these evolving complexities in dynamic fluid environments.