Nils Thuerey
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View article: P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context
P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context Open
We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations, whi…
View article: Rotational equivariant graph neural networks via local eigenbasis transformations
Rotational equivariant graph neural networks via local eigenbasis transformations Open
Rotational equivariance arises in physical problems as a common symmetry of partial differential equations, including the Navier–Stokes equations governing fluid phenomena. Architectural changes are necessary when guaranteeing rotational e…
View article: PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations
PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations Open
We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for l…
View article: Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks
Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks Open
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which rel…
View article: PRDP: Progressively Refined Differentiable Physics
PRDP: Progressively Refined Differentiable Physics Open
The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show…
View article: Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems
Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems Open
Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…
View article: Light Transport-aware Diffusion Posterior Sampling for Single-View Reconstruction of 3D Volumes
Light Transport-aware Diffusion Posterior Sampling for Single-View Reconstruction of 3D Volumes Open
We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion…
View article: APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs
APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs Open
We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly i…
View article: Flow Matching for Posterior Inference with Simulator Feedback
Flow Matching for Posterior Inference with Simulator Feedback Open
Flow-based generative modeling is a powerful tool for solving inverse problems in physical sciences that can be used for sampling and likelihood evaluation with much lower inference times than traditional methods. We propose to refine flow…
View article: ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks
ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks Open
The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equ…
View article: The Unreasonable Effectiveness of Solving Inverse Problems with Neural Networks
The Unreasonable Effectiveness of Solving Inverse Problems with Neural Networks Open
Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse probl…
View article: Linear and nonlinear flame response prediction of turbulent flames using neural network models
Linear and nonlinear flame response prediction of turbulent flames using neural network models Open
Modelling the flame response of turbulent flames via data-driven approaches is challenging due, among others, to the presence of combustion noise. Neural network methods have shown good potential to infer laminar flames’ linear and nonline…
View article: Physics-embedded Fourier Neural Network for Partial Differential Equations
Physics-embedded Fourier Neural Network for Partial Differential Equations Open
We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for ap…
View article: Stabilizing Backpropagation Through Time to Learn Complex Physics
Stabilizing Backpropagation Through Time to Learn Complex Physics Open
Of all the vector fields surrounding the minima of recurrent learning setups, the gradient field with its exploding and vanishing updates appears a poor choice for optimization, offering little beyond efficient computability. We seek to im…
View article: Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics
Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics Open
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computation…
View article: Deep learning-based predictive modelling of transonic flow over an aerofoil
Deep learning-based predictive modelling of transonic flow over an aerofoil Open
Effectively predicting transonic unsteady flow over an aerofoil poses inherent challenges. In this study, we harness the power of deep neural network (DNN) models using the attention U-Net architecture. Through efficient training of these …
View article: \Phi_\textrm{ML}: Intuitive Scientific Computing withDimension Types for Jax, PyTorch, TensorFlow & NumPy
\Phi_\textrm{ML}: Intuitive Scientific Computing withDimension Types for Jax, PyTorch, TensorFlow & NumPy Open
Φ ML is a math and neural network library designed for science applications.It enables users to quickly evaluate many network architectures on their data sets, perform (sparse) linear and non-linear optimization, and write differentiable s…
View article: Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics
Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics Open
Unrolling training trajectories over time strongly influences the inference accuracy of neural network-augmented physics simulators. We analyze this in three variants of training neural time-steppers. In addition to one-step setups and ful…
View article: Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models
Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models Open
Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging. T…
View article: Physics-Preserving AI-Accelerated Simulations of Plasma Turbulence
Physics-Preserving AI-Accelerated Simulations of Plasma Turbulence Open
Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy Simulat…
View article: High resolution dataset for flow past arbitrary bodies
High resolution dataset for flow past arbitrary bodies Open
This dataset comprises the high-resolution (768 x 512) flowfields for incompressible flow past arbitrarily shaped bodies at low Reynolds number (100, approx.) obtained using FoamExtend based immersed boundary method. The dataset is divided…
View article: Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation
Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation Open
Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a persi…
View article: Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs
Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs Open
Simulations that produce three-dimensional data are ubiquitous in science, ranging from fluid flows to plasma physics. We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth dist…
View article: Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs
Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs Open
This archive contains volumetric data from different PDE simulations. It can be used to train and evaluate the similarity assessment of different metrics.
View article: Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision
Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision Open
We address the challenging problem of jointly inferring the 3D flow and volumetric densities moving in a fluid from a monocular input video with a deep neural network. Despite the complexity of this task, we show that it is possible to tra…
View article: Solving Inverse Physics Problems with Score Matching
Solving Inverse Physics Problems with Score Matching Open
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an approxi…
View article: Exploring Physical Latent Spaces for High-Resolution Flow Restoration
Exploring Physical Latent Spaces for High-Resolution Flow Restoration Open
We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work, th…
View article: Incomplete to complete multiphysics forecasting: a hybrid approach for learning unknown phenomena
Incomplete to complete multiphysics forecasting: a hybrid approach for learning unknown phenomena Open
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural …