Stephan Simonis

Roberto Molinaro, Samuel Lanthaler, Bogdan Raonić et al.

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional score-based diffusion model. Through extensive numerical experimentation with a set of challenging fluid flows, we demonstrate that GenCFD provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of deterministic ML algorithms, trained to minimize mean square errors, regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the mathematically relevant features of turbulent fluid flows while being amenable to explicit analytical formulae. Our codes are publicly available at https://github.com/camlab-ethz/GenCFD.

Stephan Simonis, Gauthier Wissocq

The simulation of extreme Mach astrophysical flows is traditionally viewed through the lens of deterministic positivity-preserving schemes. However, due to phenomena such as Kelvin--Helmholtz instabilities and shock anomalies, the multi-dimensional Euler equations admit a plethora of non-unique entropy solutions in turbulent regimes. For the first time, we computationally explore the weak-strong uniqueness of a Mach 2000 jet by defining the statistical solution as the pushforward of a probability measure through a vectorial lattice Boltzmann method (VLBM) operator. Utilizing highly optimized CUDA kernels, we compute an ensemble of 1000 Monte Carlo samples across a sequence of unprecedentedly refined spatial grids of up to 3.2 million cells, and subsequently post-process the empirical measures via memory-mapped CPU streaming. We contrast the strong sample-wise $L^1$ error divergence with the convergence of the probability measure in the 1-point Wasserstein distance via empirical Cauchy rates. Our mathematical results demonstrate that while individual flow realizations physically diverge due to chaotic shear-layer instabilities, the macroscopic statistical solution converges to a well-defined limit measure at a rate of 0.5. Conclusively, we provide the first numerical verification of statistical solution stability in the extreme compressible regime.

Dennis Teutscher, Tyll Weber-Carstanjen, Stephan Simonis et al.

Efficient solid-liquid separation is crucial in industries like mining, but traditional chamber filter presses depend heavily on manual monitoring, leading to inefficiencies, downtime, and resource wastage. This paper introduces a machine learning-powered digital twin framework to improve operational flexibility and predictive control. A key challenge addressed is the degradation of the filter medium due to repeated cycles and clogging, which reduces filtration efficiency. To solve this, a neural network-based predictive model was developed to forecast operational parameters, such as pressure and flow rates, under various conditions. This predictive capability allows for optimized filtration cycles, reduced downtime, and improved process efficiency. Additionally, the model predicts the filter mediums lifespan, aiding in maintenance planning and resource sustainability. The digital twin framework enables seamless data exchange between filter press sensors and the predictive model, ensuring continuous updates to the training data and enhancing accuracy over time. Two neural network architectures, feedforward and recurrent, were evaluated. The recurrent neural network outperformed the feedforward model, demonstrating superior generalization. It achieved a relative $L^2$-norm error of $5\%$ for pressure and $9.3\%$ for flow rate prediction on partially known data. For completely unknown data, the relative errors were $18.4\%$ and $15.4\%$, respectively. Qualitative analysis showed strong alignment between predicted and measured data, with deviations within a confidence band of $8.2\%$ for pressure and $4.8\%$ for flow rate predictions. This work contributes an accurate predictive model, a new approach to predicting filter medium cycle impacts, and a real-time interface for model updates, ensuring adaptability to changing operational conditions.