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Title: Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Video

Paper content:
We propose a model that is able to perform physical parameter estimation of systems from video, where the differential equations governing the scene dynamics are known, but labeled states or objects are not available.
Existing physical scene understanding methods require either object state supervision, or do not integrate with differentiable physics to learn interpretable system parameters and states.
We address this problem through a \textit{physics-as-inverse-graphics} approach that brings together vision-as-inverse-graphics and differentiable physics engines, where objects and explicit state and velocity representations are discovered by the model.
This framework allows us to perform long term extrapolative video prediction, as well as vision-based model-predictive control.
Our approach significantly outperforms related unsupervised methods in long-term future frame prediction of systems with interacting objects (such as ball-spring or 3-body gravitational systems), due to its ability to build dynamics into the model as an inductive bias.
We further show the value of this tight vision-physics integration by demonstrating data-efficient learning of vision-actuated model-based control for a pendulum system.
We also show that the controller's interpretability provides unique capabilities in goal-driven control and physical reasoning for zero-data adaptation.
System identification or physical parameter estimation is commonly required for control or state estimation for physical modelling, and typically relies on dedicated sensing equipment and carefully constructed experiments.
Current machine learning approaches to physical modeling from video either require training by supervised regression from video to object coordinates before estimating explicit physics (Watters et al., 2017; Wu et al., 2017b; Belbute-Peres et al., 2018) , or are able to discover and segment objects from video in an unsupervised manner, but do not naturally integrate with a physics engine for long-term predictions or generation of interpretable locations and physical parameters for physical reasoning (Xu et al., 2019; van Steenkiste et al., 2018) .
In this work, we bridge the gap between unsupervised discovery of objects from video and learning the physical dynamics of a system, by learning unknown physical parameters and explicit trajectory coordinates.
Our approach, called physics-as-inverse-graphics, solves the physical modeling problem via a novel vision-as-inverse-graphics encoder-decoder system that can render and de-render image components using Spatial Transformers (ST) (Jaderberg et al., 2015) in a way that makes it possible for the latent representation to generate disentangled interpretable states (position/velocity).
These can be used directly by a differentiable physics engine (Degrave et al., 2016; Belbute-Peres et al., 2018) to learn the parameters of a scene where the family of differential equations governing the system are known (e.g. objects connected by a spring), but the corresponding parameters are not (e.g. spring constant).
This allows us to to identify physical parameters and learn vision components of the model jointly in an end-to-end fashion.
Our contribution is a solution to unsupervised learning of physical parameters from video, without having access to ground-truth appearance, position or velocities of the objects, a task that had so far remained unsolved (Wu et al., 2015; Belbute-Peres et al., 2018) .
In addition to showing that our model can learn physical parameters without object or state supervision (a task with intrinsic scientific interest in and of itself), we show that incorporating dynamics priors in the form of known physical equations of motion with learnable parameters together with learnable vision and graphics can improve model performance in two challenging tasks: long term video prediction and visual model predictive control.
We first evaluate physical parameter estimation accuracy and future video frame prediction on 4 datasets with different non-linear interactions and visual difficulty.
We then demonstrate the value of our method by applying it for data-efficient learning of vision-based control of an under-actuated pendulum.
Notably our unique ability to extract interpretable states and parameters from pixels without supervision enables end-to-end vision-based control to exploit goal-paramaterized policies and physical reasoning for zero-shot adaptation.
Physics-as-inverse graphics provides a valuable mechanism to integrate inductive bias about physical data generating processes into learning.
This allows unsupervised object tracking and system identification, in addition to sample efficient, generalisable and flexible control.
However, incorporating this structure into lightly supervised deep learning models has proven challenging to date.
We introduced a model that accomplishes this, relying on a coordinate-consistent decoder that enables image reconstruction from physics.
We have shown that our model is able to perform accurate long term prediction and that it can be used to learn the dynamics of an actuated system, allowing us to perform vision-based model-predictive control.

assistant: text: We propose a model that is able to perform physical parameter estimation of systems from video, where the differential equations governing the scene dynamics are known, but labeled states or objects are not available.