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NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework

Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Max Rietmann, Jose del Aguila Ferrandis, Wonmin Byeon, Zhiwei Fang, Sanjay Choudhry

arXiv:2012.07938v1physics.flu-dyncs.LG

TL;DR

Simulations can become computationally expensive as geometries, physics, and design evaluations grow, and conventional neural networks may require costly training data or struggle with complex real-world domains. SimNet combines physics-driven neural-network solvers with parameterized geometries and physics to address forward, inverse, and data-assimilation problems. The paper reports good correlation with open-source and commercial solvers, while noting that broader applications are still needed to verify robustness and applicability.

  • Problem

    Complex simulations can be costly, while supervised neural networks require expensive data and prior solver examples largely covered simple domains rather than complex 3D multi-physics applications.

    Source: §1 · pp. 1–2

  • Method

    SimNet is an AI-driven framework that combines physics-driven neural-network solvers with parameterized geometry and physics for forward, inverse, and data-assimilation simulations.

    Source: §1 · p. 2, §7 · pp. 13–14

  • Results

    SimNet results show good correlation with open-source and commercial solvers, and the framework addresses high-Reynolds-number turbulent industrial flows without training data.

    Source: §7 · p. 14

  • Takeaways & Limitations

    Parameterized geometry lets one training cover the supplied design-parameter range, with inference for a design configuration completed in real time.

    Source: §7 · p. 14

    Further applications across a wide range of use cases are needed to verify neural-network solvers’ robustness, accuracy, and applicability.

    Source: §7 · p. 14

Abstract

from arXiv · show

We present SimNet, an AI-driven multi-physics simulation framework, to accelerate simulations across a wide range of disciplines in science and engineering. Compared to traditional numerical solvers, SimNet addresses a wide range of use cases - coupled forward simulations without any training data, inverse and data assimilation problems. SimNet offers fast turnaround time by enabling parameterized system representation that solves for multiple configurations simultaneously, as opposed to the traditional solvers that solve for one configuration at a time. SimNet is integrated with parameterized constructive solid geometry as well as STL modules to generate point clouds. Furthermore, it is customizable with APIs that enable user extensions to geometry, physics and network architecture. It has advanced network architectures that are optimized for high-performance GPU computing, and offers scalable performance for multi-GPU and multi-Node implementation with accelerated linear algebra as well as FP32, FP64 and TF32 computations. In this paper we review the neural network solver methodology, the SimNet architecture, and the various features that are needed for effective solution of the PDEs. We present real-world use cases that range from challenging forward multi-physics simulations with turbulence and complex 3D geometries, to industrial design optimization and inverse problems that are not addressed efficiently by the traditional solvers. Extensive comparisons of SimNet results with open source and commercial solvers show good correlation.

1 Introduction

Simulations become costly as geometry, model size, physics complexity, or design evaluations grow, while data-driven neural networks can require expensive data and may not respect governing physics. SimNet is presented as a framework for complex real-world problems, including parameterized design optimization and physics-driven solver applications.

1 Introduction

  • Simulation costs rise with geometry detail, model size, physical complexity, and design evaluations, while single runs can take hours or days.The passage also notes that supervised data-driven neural networks require costly data and may violate governing physics or generalize unreliably.Source: §1 · p. 1
  • Neural network solvers can run parameterized simulations in one run and address inverse or data-assimilation problems without training data for forward solves.Data constraints are added to the loss for inverse or data-assimilation problems.Source: §1 · p. 2
  • Earlier neural-network solver examples and libraries were mostly limited to simple 1D or 2D domains, while SimNet targets complex 3D geometries and multi-physics.The passage gives FPGA heat-sink design optimization as an example of a single training without training data.Source: §1 · p. 2
  • The FPGA heat-sink optimization varies center and side fin heights, with intermediate fin heights transitioning linearly.Source: Figure 1 · p. 2
  • SimNet’s stated features include SDF loss weighting, integral continuity planes, advanced architectures, geometry point-cloud modules, and geometry and physics parameterization.The authors also report solving industrial high-Reynolds-number flows with a zero-equation turbulence model without data.Source: §1 · p. 2

2 AI driven Simulations

The section describes four areas where neural-network solvers may serve computational science and engineering: design exploration, improved physics predictions, inverse modeling, and real-time simulation. These applications address simulation limits around design-cycle resources, model fidelity, unavailable boundary conditions, and immediate feedback.

Design Space Exploration and Optimization

  • Neural-network surrogates support design-space exploration across multiple geometries or parameterized designs when time and compute resources limit conventional simulations.The passage frames this as a way to provide engineers faster feedback on designs.Source: §2 · p. 3

Improved physics and predictions

  • Neural networks can learn viscosity or turbulence models from high-fidelity results or experiments for use in lower-cost solver frameworks.The section also names radiation and micromechanics as other candidate physics areas.Source: §2 · p. 3

Inverse Modeling

  • Neural-network solvers can infer physical quantities from observational data and offer an alternative when boundary conditions are not readily available.Examples include recovering subsurface velocity from recorded sound and estimating flow quantities from medical images.Source: §2 · p. 3

Real-Time Simulations

  • A pretrained neural-network solver can provide feedback in seconds for applications requiring near-instantaneous simulation, including robotics and autonomous driving.Source: §2 · p. 3

3 Neural Network Solvers

A neural-network solver approximates a PDE solution with a feed-forward network and trains it to satisfy both the governing equation and initial or boundary constraints. Its loss combines PDE and constraint residuals, which are weighted and minimized through iterative optimization.

3 Neural Network Solvers

  • A neural-network solver approximates a PDE solution with a feed-forward fully connected network, trained to minimize a loss for the PDE and its constraints.Source: §3 · p. 4
  • The formulation defines differential operators over a domain, a solution u(x), and constraint operators that usually specify boundary and initial conditions.The network’s input encoding may be the identity, yielding a standard fully connected architecture.Source: §3 · p. 4
  • The loss penalizes PDE residuals and encodes constraints as penalty terms, with weighting functions controlling the balance among loss terms.Source: §3 · pp. 4–5
  • Network parameters are iteratively optimized with stochastic-gradient methods such as Adam, while loss integrals are estimated by regular or Quasi-Monte Carlo sampling.Automatic differentiation computes the gradients required for the loss.Source: §3 · p. 5

4 SimNet Overview

SimNet assembles geometry, PDEs, data, network architecture, and optimization choices into a neural-network solver workflow. Its geometry, physics, and network modules provide tools for complex domains, loss weighting, continuity constraints, and specialized architectures.

4 SimNet Overview

  • SimNet combines geometry, PDE, and data inputs with a user-selected network, optimizer, and learning-rate schedule, then trains or runs inference on one GPU or a GPU cluster.Outputs can be saved as CSV or VTK files and visualized with TensorBoard or ParaView.Source: §4 · p. 5

4.1 Geometry modules

  • CSG primitives and Boolean operations support parameterized shapes for design optimization, while the tessellated-geometry module imports STL, OBJ, and other complex geometries.The CSG module also generates quasi-random Halton point clouds for quasi-Monte Carlo loss approximation; continuous sampling offers similar accuracy to fixed point clouds without their generation cost.Source: §4.1 · pp. 5–6
  • Signed-distance weighting assigns spatially varying loss weights and can reduce the effects of sharp local gradients, often improving convergence speed and sometimes accuracy.For tessellated meshes, a custom OptiX library accelerates inside/outside testing and distance computation using ray intersections, triangle normals, and a bounding-volume hierarchy.Source: §4.1 · pp. 5–6

4.2 PDE module

  • The PDE module includes common equations and uses SymPy to let users define equations; its zero-equation turbulence model computes turbulent viscosity using wall distance and its spatial derivatives.More advanced turbulence models can also be implemented in the framework.Source: §4.2 · p. 6
  • Integral continuity planes impose volumetric flow rates at outlets and across channels, which significantly speeds convergence and improves accuracy; exact continuity can improve convergence and accuracy but adds training time through third-order derivatives.The exact-continuity formulation uses a vector-potential velocity field that is divergence-free.Source: §4.2 · pp. 6–7

4.3 Network architectures

  • Fourier feature networks use trainable high-frequency input encodings to address neural networks’ bias toward low-frequency solutions.The trainable frequency matrix specifies the encoding’s frequency sets.Source: §4.3 · p. 7
  • SimNet’s modified Fourier feature network projects Fourier features into a learned space and combines them with hidden layers through element-wise multiplication, potentially improving convergence and accuracy at slightly greater iteration time.The architecture is presented as novel to SimNet.Source: §4.3 · p. 7
  • SiReNs use sinusoidal activations, with a first-layer scaling factor that spans multiple sine periods and an initialization scheme intended to preserve activation distributions in deep networks.The default first-layer scaling factor is 30.Source: §4.3 · p. 7

5 Use Cases

SimNet is applied to time-independent forward multi-physics problems, complex aneurysm geometry, design optimization, and inverse modeling. Parameterized inference enables rapid evaluation of many heat-sink designs, while a hybrid data-and-physics loss supports inference of unknown flow properties.

5 Use Cases

  • The showcased use cases are time-independent; cases 5.1–5.3 are forward simulations without training data, while a more efficient and accurate convolutional-LSTM approach for transient simulations remains under development..Source: §5 · pp. 7–8

5.1 Turbulent and multi-physics simulations

  • At Re = 13,239.6, SimNet solves FPGA conjugate heat transfer with separate flow and temperature networks; Fourier variants converge better than SiReN, while unweighted Fourier and fully connected models fail to converge reasonably.The loss curves compare architectures, and the fields are visualized for the modified Fourier feature network.Source: §5.1 · p. 8, Figure 6 · p. 9

5.2 Blood flow in an Intracranial Aneurysm

  • For a patient-specific aneurysm, SimNet solves the forward problem without training data and captures the flow field, including flow development inside the aneurysm sac.The results include velocity magnitude and pressure distributions.Source: §5.2 · pp. 8–9, Figure 9 · p. 11

5.3 Design optimization for multi-physics industrial systems

  • 531,441 designs are evaluated from combinations of three spatial and nine geometry parameters, selecting the configuration with minimum peak temperature subject to a pressure-drop constraint.The parameterized models are trained before evaluating the design combinations.Source: §5.3 · p. 9
  • On the NVSwitch base geometry, OpenFOAM overpredicts commercial-solver results by 4.5%, while SimNet underpredicts them by about 15%.The comparison concerns pressure drop and peak temperature.Source: §5.3 · pp. 9–10, Table 2 · p. 10
  • SimNet accelerates NVSwitch design optimization by 45,000x versus the commercial solver and 135,000x versus OpenFOAM.The reported total compute-time comparison is for the design optimization task.Source: §5.3 · p. 10, Table 3 · p. 12

5.4 Inverse problems

  • With synthetic OpenFOAM measurements sampled only in the heat-sink wake, a hybrid data-and-PDE loss fits u, v, p, and T while inferring flow viscosity and thermal diffusivity.The governing equations include Navier–Stokes and advection–diffusion.Source: §5.4 · p. 12

6 Performance Upgrades and Multi-GPU Training

SimNet uses XLA kernel fusion, multi-GPU training with learning-rate warmup, and TF32 math mode to improve training performance. Experiments report up to 3.3x faster single iterations with XLA and hardware-dependent TF32 speedups while retaining similar accuracy to FP32.

6.1 XLA compiler

  • XLA kernel fusion accelerates a single SimNet training iteration by up to 3.3x on the FPGA problem.XLA fuses point-wise operations into fewer GPU kernels, reducing memory transfers.Source: §6.1 · pp. 12–13

6.2 Learning rate scaling in multi-GPU training

  • Multi-GPU training combines data parallelism with learning-rate warmup and scaling; the time per iteration remains nearly constant as batch size grows, and warmup helps prevent early divergence.The reported NVSwitch training examines scaling from 1 to 16 GPUs.Source: §6.2 · p. 13

6.3 TF32 math mode

  • TF32 yields up to 1.6x speed-up over FP32 on A100 GPUs and up to 3.1x speed-up over FP32 on V100 GPUs, with similar accuracy.These results are from the FPGA heat-sink problem.Source: §6.3 · p. 13

7 Conclusion

SimNet combines neural-network simulation features for real-world geometries and multiple physics with parameterized design evaluation. Comparisons show good correlation with open-source and commercial solvers, while broader applications are still needed to verify robustness, accuracy, and applicability.

7 Conclusion

  • SimNet supports forward, inverse, and data-assimilation problems for real-world geometries and multiple physics without training data.SDF-based loss weighting is used to improve training convergence in cases involving sharp geometric corners and gradients.Source: §7 · p. 13
  • The conclusion includes figures on weak scaling on V100 GPUs and accelerated training on A100 GPUs.The supplied passages provide figure titles but no results to report.Source: Figure 14 · p. 14, Figure 15 · p. 14
  • SimNet’s TG module imports tessellated geometries from CAD, while Navier–Stokes simulations impose continuity globally and locally.The passage reports high-Reynolds-number turbulent-flow simulations for industrial applications and calls this, to the authors’ knowledge, the first such physics-driven neural-network application.Source: §7 · p. 14
  • Parameterized CSG geometry lets one training cover the given parameter range, with real-time inference for a design configuration.The passage states this accelerates neural-network simulations by orders of magnitude compared with traditional simulations run one at a time.Source: §7 · p. 14
  • SimNet results correlate well with open-source and commercial solvers, but further applications are needed to verify robustness, accuracy, and applicability.The conclusion frames those further applications as necessary for verification across a wide range of use cases.Source: §7 · p. 14

A FPGA Problem Description

The FPGA geometry dimensions are normalized by setting the channel height to 1. The channel walls are adiabatic, and interface boundary conditions apply at the fluid-solid interface.

A FPGA Problem Description

B Aneurysm Problem Description

The aneurysm simulation uses no-slip walls, a parabolic inlet, and a zero-pressure outlet. The problem uses a constant fluid density of 1.0 and about 20 million training points.

B Aneurysm Problem Description

C NVSwitch Problem Description

The channel simulation specifies its inlet, outlet, wall, and thermal conditions. The NVSwitch fin design varies fin thickness, front and back fin lengths, and trim angles under an assumed maximum pressure drop.

C NVSwitch Problem Description

D Learning Rate Linear Warm-up

The section specifies a linear warm-up learning-rate scheme for runs using n_g GPUs, built on a baseline exponential-decay schedule. It defines the baseline schedule parameters and the number of warm-up steps.

D Learning Rate Linear Warm-up

  • The learning rate η at step s is specified for the linear warm-up scheme when run with n_g GPUs.The passage introduces the schedule but does not state its formula in the supplied text.Source: D Learning Rate Linear Warm-up · p. 17
  • The warm-up scheme uses η_b, the baseline exponential-decay learning-rate schedule.The baseline schedule is introduced separately.Source: D Learning Rate Linear Warm-up · p. 17
  • The baseline schedule uses decay steps s_d, decay rate r, start and end rates η_0,b and η_1,b, and warm-up steps s_w.The passage defines these schedule parameters.Source: D Learning Rate Linear Warm-up · p. 17
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