# Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations

arXiv: https://arxiv.org/abs/2205.01222 · HTML: https://mlsanity.com/paper/2205.01222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 64 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Learning Neural PDE Solvers with Convergence Guarantees](https://mlsanity.com/paper/1906.01200/) (2019)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data](https://mlsanity.com/paper/1808.04327/) (2018)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [Liquid Splash Modeling with Neural Networks](https://mlsanity.com/paper/1704.04456/) (2017)

## Built on by (most cited first, 3 of 3)

- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Solving Inverse Physics Problems with Score Matching](https://mlsanity.com/paper/2301.10250/) (2023)
- [Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics](https://mlsanity.com/paper/2305.14286/) (2023)

## Abstract (arXiv)

We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing complexity: We show that BNNs, when used as surrogate models for steady-state fluid flow predictions, provide accurate physical predictions together with sensible estimates of uncertainty. Further, we experiment with perturbed temporal sequences from Navier-Stokes simulations and evaluate the capabilities of BNNs to capture multimodal evolutions. While our findings indicate that this is problematic for large perturbations, our results show that the networks learn to correctly predict high uncertainties in such situations. Finally, we study BNNs in the context of solver interactions with turbulent plasma flows. We find that BNN-based corrector networks can stabilize coarse-grained simulations and successfully create multimodal trajectories.