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A Review of Differentiable Simulators

Rhys Newbury, Jack Collins, Kerry He, Jiahe Pan, Ingmar Posner, David Howard, Akansel Cosgun

TL;DR

An in-depth review of the evolving landscape of differentiable physics simulators is presented, highlighting current limitations as well as providing insights into future directions for the field.

Abstract

Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which allows differentiable simulators to be readily integrated into commonly employed gradient-based optimization schemes. To achieve this, a number of design decisions need to be considered representing trade-offs in versatility, computational speed, and accuracy of the gradients obtained. This paper presents an in-depth review of the evolving landscape of differentiable physics simulators. We introduce the foundations and core components of differentiable simulators alongside common design choices. This is followed by a practical guide and overview of open-source differentiable simulators that have been used across past research. Finally, we review and contextualize prominent applications of differentiable simulation. By offering a comprehensive review of the current state-of-the-art in differentiable simulation, this work aims to serve as a resource for researchers and practitioners looking to understand and integrate differentiable physics within their research. We conclude by highlighting current limitations as well as providing insights into future directions for the field.

A Review of Differentiable Simulators

TL;DR

An in-depth review of the evolving landscape of differentiable physics simulators is presented, highlighting current limitations as well as providing insights into future directions for the field.

Abstract

Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which allows differentiable simulators to be readily integrated into commonly employed gradient-based optimization schemes. To achieve this, a number of design decisions need to be considered representing trade-offs in versatility, computational speed, and accuracy of the gradients obtained. This paper presents an in-depth review of the evolving landscape of differentiable physics simulators. We introduce the foundations and core components of differentiable simulators alongside common design choices. This is followed by a practical guide and overview of open-source differentiable simulators that have been used across past research. Finally, we review and contextualize prominent applications of differentiable simulation. By offering a comprehensive review of the current state-of-the-art in differentiable simulation, this work aims to serve as a resource for researchers and practitioners looking to understand and integrate differentiable physics within their research. We conclude by highlighting current limitations as well as providing insights into future directions for the field.
Paper Structure (55 sections, 21 equations, 10 figures, 2 tables)

This paper contains 55 sections, 21 equations, 10 figures, 2 tables.

Table of Contents

  1. Definition
  2. Gradients
  3. Dynamical Model
  4. Integrator
  5. Coordinate Sytem
  6. Type
  7. Application Type
  8. Open Source
  9. Documentation
  10. Actively Maintained
  11. Language
  12. Introduction
  13. Foundations of Differentiable Simulators
  14. Gradient Calculation
  15. Automatic Differentiation
  16. ...and 40 more sections

Figures (10)

  • Figure 1: A visualization of the breadth of published research progressing the field of differentiable simulation. Areas and applications of differentiable simulators cover topics such as soft and rigid-body simulation; system identification; trajectory optimization; morphology optimization; and many others covered in-detail in this review degrave-2019-a-roboticshu-2020-difftaichi-simulationgeilinger-2020-add-contactdu-2021-diffpd-dynamicsjatavallabhula-2021-gradsim-controlhuang-2021-plasticinelab-physicsheiden-2021-disect-cuttingXu-2021-An-Designli-2023-dexdeform-physicsli-2022-diffcloth-contact and hu-2019-chainqueen-roboticslutter-2021-differentiable-learning(© 2024 IEEE)
  • Figure 2: An overview of how the different components of a differentiable simulator interact. Each of these components (except for the loss function and gradient optimizer) are explored in detail in \ref{['sec:differentiable_physics']}.
  • Figure 3: Comparison between (a) the second-order frictional cone defining Coulomb's law (see \ref{['eqn:friction-cone']}), and (b) the square pyramid which linearizes the cone for LCP. Note that the linearized cone biases frictional forces towards the edges of the pyramid.
  • Figure 4: Comparison of different contact model implementations. The non-penetration requirements and Coulomb's friction law do not have well-defined gradients at $q_n=0$ and $\norm{\dot{q}_t}=0$, respectively. Compliant models relax these models by approximating the discontinuities, which we can consider as impulse function-like gradients, using functions with finite but sufficiently large gradients.
  • Figure 5: An Area-Proportional Venn diagram larsson-2018-case-eulerr visualizing the different application areas of differentiable simulators explored in this review with the numbers indicating the number of referenced works. The number of cited works for a given application area in the Venn diagram is cumulative.
  • ...and 5 more figures