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We present a differentiable physics engine that can be integrated as a module in deep neural networks for end-to-end learning. As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency. Specifically, in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem. Unlike traditional finite difference methods, such gradients can be computed analytically, which allows for greater flexibility of the engine. Through experiments in diverse domains, we highlight the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods. Code for the engine and experiments is included with the paper.
Author Information
Filipe de Avila Belbute Peres (Carnegie Mellon University)
Kevin Smith (MIT)
Kelsey Allen (MIT)
Josh Tenenbaum (MIT)
Josh Tenenbaum is an Associate Professor of Computational Cognitive Science at MIT in the Department of Brain and Cognitive Sciences and the Computer Science and Artificial Intelligence Laboratory (CSAIL). He received his PhD from MIT in 1999, and was an Assistant Professor at Stanford University from 1999 to 2002. He studies learning and inference in humans and machines, with the twin goals of understanding human intelligence in computational terms and bringing computers closer to human capacities. He focuses on problems of inductive generalization from limited data -- learning concepts and word meanings, inferring causal relations or goals -- and learning abstract knowledge that supports these inductive leaps in the form of probabilistic generative models or 'intuitive theories'. He has also developed several novel machine learning methods inspired by human learning and perception, most notably Isomap, an approach to unsupervised learning of nonlinear manifolds in high-dimensional data. He has been Associate Editor for the journal Cognitive Science, has been active on program committees for the CogSci and NIPS conferences, and has co-organized a number of workshops, tutorials and summer schools in human and machine learning. Several of his papers have received outstanding paper awards or best student paper awards at the IEEE Computer Vision and Pattern Recognition (CVPR), NIPS, and Cognitive Science conferences. He is the recipient of the New Investigator Award from the Society for Mathematical Psychology (2005), the Early Investigator Award from the Society of Experimental Psychologists (2007), and the Distinguished Scientific Award for Early Career Contribution to Psychology (in the area of cognition and human learning) from the American Psychological Association (2008).
J. Zico Kolter (Carnegie Mellon University / Bosch Center for AI)
Zico Kolter is an Assistant Professor in the School of Computer Science at Carnegie Mellon University, and also serves as Chief Scientist of AI Research for the Bosch Center for Artificial Intelligence. His work focuses on the intersection of machine learning and optimization, with a large focus on developing more robust, explainable, and rigorous methods in deep learning. In addition, he has worked on a number of application areas, highlighted by work on sustainability and smart energy systems. He is the recipient of the DARPA Young Faculty Award, and best paper awards at KDD, IJCAI, and PESGM.
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2017 Oral: Gradient descent GAN optimization is locally stable »
Vaishnavh Nagarajan · J. Zico Kolter -
2017 Poster: MarrNet: 3D Shape Reconstruction via 2.5D Sketches »
Jiajun Wu · Yifan Wang · Tianfan Xue · Xingyuan Sun · Bill Freeman · Josh Tenenbaum -
2017 Poster: Self-Supervised Intrinsic Image Decomposition »
Michael Janner · Jiajun Wu · Tejas Kulkarni · Ilker Yildirim · Josh Tenenbaum -
2017 Poster: Task-based End-to-end Model Learning in Stochastic Optimization »
Priya Donti · J. Zico Kolter · Brandon Amos -
2017 Tutorial: Engineering and Reverse-Engineering Intelligence Using Probabilistic Programs, Program Induction, and Deep Learning »
Josh Tenenbaum · Vikash Mansinghka -
2016 : Datasets, Methodology, and Challenges in Intuitive Physics »
Emmanuel Dupoux · Josh Tenenbaum -
2016 : Josh Tenenbaum »
Josh Tenenbaum -
2016 : Reverse engineering human cooperation (or, How to build machines that treat people like people) »
Josh Tenenbaum · Max Kleiman-Weiner -
2016 : Naive Physics 101: A Tutorial »
Emmanuel Dupoux · Josh Tenenbaum -
2016 : Opening Remarks »
Josh Tenenbaum -
2016 Workshop: Intuitive Physics »
Adam Lerer · Jiajun Wu · Josh Tenenbaum · Emmanuel Dupoux · Rob Fergus -
2016 Poster: The Multiple Quantile Graphical Model »
Alnur Ali · J. Zico Kolter · Ryan Tibshirani -
2016 Poster: Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation »
Tejas Kulkarni · Karthik Narasimhan · Ardavan Saeedi · Josh Tenenbaum -
2016 Poster: Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling »
Jiajun Wu · Chengkai Zhang · Tianfan Xue · Bill Freeman · Josh Tenenbaum -
2016 Poster: Sampling for Bayesian Program Learning »
Kevin Ellis · Armando Solar-Lezama · Josh Tenenbaum -
2016 Poster: Probing the Compositionality of Intuitive Functions »
Eric Schulz · Josh Tenenbaum · David Duvenaud · Maarten Speekenbrink · Samuel J Gershman -
2015 Workshop: Black box learning and inference »
Josh Tenenbaum · Jan-Willem van de Meent · Tejas Kulkarni · S. M. Ali Eslami · Brooks Paige · Frank Wood · Zoubin Ghahramani -
2015 : Discussion Panel with Morning Speakers (Day 1) »
Pedro Domingos · Stephen H Muggleton · Rina Dechter · Josh Tenenbaum -
2015 : Cognitive Foundations for Common-Sense Knowledge Representation and Reasoning »
Josh Tenenbaum -
2015 Poster: Softstar: Heuristic-Guided Probabilistic Inference »
Mathew Monfort · Brenden M Lake · Brenden Lake · Brian Ziebart · Patrick Lucey · Josh Tenenbaum -
2015 Poster: Deep Convolutional Inverse Graphics Network »
Tejas Kulkarni · William Whitney · Pushmeet Kohli · Josh Tenenbaum -
2015 Spotlight: Deep Convolutional Inverse Graphics Network »
Tejas Kulkarni · William Whitney · Pushmeet Kohli · Josh Tenenbaum -
2015 Poster: Galileo: Perceiving Physical Object Properties by Integrating a Physics Engine with Deep Learning »
Jiajun Wu · Ilker Yildirim · Joseph Lim · Bill Freeman · Josh Tenenbaum -
2015 Poster: Unsupervised Learning by Program Synthesis »
Kevin Ellis · Armando Solar-Lezama · Josh Tenenbaum -
2014 Workshop: 3rd NIPS Workshop on Probabilistic Programming »
Daniel Roy · Josh Tenenbaum · Thomas Dietterich · Stuart J Russell · YI WU · Ulrik R Beierholm · Alp Kucukelbir · Zenna Tavares · Yura Perov · Daniel Lee · Brian Ruttenberg · Sameer Singh · Michael Hughes · Marco Gaboardi · Alexey Radul · Vikash Mansinghka · Frank Wood · Sebastian Riedel · Prakash Panangaden -
2013 Workshop: Machine Learning for Sustainability »
Edwin Bonilla · Thomas Dietterich · Theodoros Damoulas · Andreas Krause · Daniel Sheldon · Iadine Chades · J. Zico Kolter · Bistra Dilkina · Carla Gomes · Hugo P Simao -
2013 Workshop: Deep Learning »
Yoshua Bengio · Hugo Larochelle · Russ Salakhutdinov · Tomas Mikolov · Matthew D Zeiler · David Mcallester · Nando de Freitas · Josh Tenenbaum · Jian Zhou · Volodymyr Mnih -
2013 Poster: One-shot learning by inverting a compositional causal process »
Brenden M Lake · Russ Salakhutdinov · Josh Tenenbaum -
2013 Poster: Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs »
Vikash Mansinghka · Tejas D Kulkarni · Yura N Perov · Josh Tenenbaum -
2013 Oral: Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs »
Vikash Mansinghka · Tejas D Kulkarni · Yura N Perov · Josh Tenenbaum -
2011 Workshop: Challenges in Learning Hierarchical Models: Transfer Learning and Optimization »
Quoc V. Le · Marc'Aurelio Ranzato · Russ Salakhutdinov · Josh Tenenbaum · Andrew Y Ng -
2011 Workshop: Machine Learning for Sustainability »
Thomas Dietterich · J. Zico Kolter · Matthew A Brown -
2011 Poster: Learning to Learn with Compound HD Models »
Russ Salakhutdinov · Josh Tenenbaum · Antonio Torralba -
2011 Spotlight: Learning to Learn with Compound HD Models »
Russ Salakhutdinov · Josh Tenenbaum · Antonio Torralba -
2011 Poster: The Fixed Points of Off-Policy TD »
J. Zico Kolter -
2011 Spotlight: The Fixed Points of Off-Policy TD »
J. Zico Kolter -
2010 Workshop: Transfer Learning Via Rich Generative Models. »
Russ Salakhutdinov · Ryan Adams · Josh Tenenbaum · Zoubin Ghahramani · Tom Griffiths -
2010 Invited Talk: How to Grow a Mind: Statistics, Structure and Abstraction »
Josh Tenenbaum -
2010 Poster: Dynamic Infinite Relational Model for Time-varying Relational Data Analysis »
Katsuhiko Ishiguro · Tomoharu Iwata · Naonori Ueda · Josh Tenenbaum -
2010 Poster: Nonparametric Bayesian Policy Priors for Reinforcement Learning »
Finale P Doshi-Velez · David Wingate · Nicholas Roy · Josh Tenenbaum -
2010 Poster: Energy Disaggregation via Discriminative Sparse Coding »
J. Zico Kolter · Siddarth Batra · Andrew Y Ng -
2009 Workshop: Bounded-rational analyses of human cognition: Bayesian models, approximate inference, and the brain »
Noah Goodman · Edward Vul · Tom Griffiths · Josh Tenenbaum -
2009 Workshop: Analyzing Networks and Learning With Graphs »
Edo M Airoldi · Jure Leskovec · Jon Kleinberg · Josh Tenenbaum -
2009 Mini Symposium: Machine Learning for Sustainability »
J. Zico Kolter · Thomas Dietterich · Andrew Y Ng -
2009 Poster: Perceptual Multistability as Markov Chain Monte Carlo Inference »
Samuel J Gershman · Edward Vul · Josh Tenenbaum -
2009 Poster: Help or Hinder: Bayesian Models of Social Goal Inference »
Tomer D Ullman · Chris L Baker · Owen Macindoe · Owain Evans · Noah Goodman · Josh Tenenbaum -
2009 Spotlight: Perceptual Multistability as Markov Chain Monte Carlo Inference »
Samuel J Gershman · Edward Vul · Josh Tenenbaum -
2009 Poster: Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model »
Edward Vul · Michael C Frank · George Alvarez · Josh Tenenbaum -
2009 Oral: Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model »
Edward Vul · Michael C Frank · George Alvarez · Josh Tenenbaum -
2009 Poster: Modelling Relational Data using Bayesian Clustered Tensor Factorization »
Ilya Sutskever · Russ Salakhutdinov · Josh Tenenbaum -
2008 Workshop: Probabilistic Programming: Universal Languages, Systems and Applications »
Daniel Roy · John Winn · David A McAllester · Vikash Mansinghka · Josh Tenenbaum -
2008 Workshop: Machine learning meets human learning »
Nathaniel D Daw · Tom Griffiths · Josh Tenenbaum · Jerry Zhu -
2007 Workshop: The Grammar of Vision: Probabilistic Grammar-Based Models for Visual Scene Understanding and Object Categorization »
Virginia Savova · Josh Tenenbaum · Leslie Kaelbling · Alan Yuille -
2007 Spotlight: A Bayesian Framework for Cross-Situational Word-Learning »
Michael C Frank · Noah Goodman · Josh Tenenbaum -
2007 Poster: A Bayesian Framework for Cross-Situational Word-Learning »
Michael C Frank · Noah Goodman · Josh Tenenbaum -
2007 Poster: A complexity measure for intuitive theories »
Charles Kemp · Noah Goodman · Josh Tenenbaum -
2007 Spotlight: Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion »
J. Zico Kolter · Pieter Abbeel · Andrew Y Ng -
2007 Poster: Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion »
J. Zico Kolter · Pieter Abbeel · Andrew Y Ng -
2006 Poster: Combining causal and similarity-based reasoning »
Charles Kemp · Patrick Shafto · Allison Berke · Josh Tenenbaum -
2006 Poster: Multiple timescales and uncertainty in motor adaptation »
Konrad P Kording · Josh Tenenbaum · Reza Shadmehr -
2006 Poster: Learning annotated hierarchies from relational data »
Daniel Roy · Charles Kemp · Vikash Mansinghka · Josh Tenenbaum -
2006 Talk: Learning annotated hierarchies from relational data »
Daniel Roy · Charles Kemp · Vikash Mansinghka · Josh Tenenbaum -
2006 Spotlight: Multiple timescales and uncertainty in motor adaptation »
Konrad P Kording · Josh Tenenbaum · Reza Shadmehr -
2006 Talk: Combining causal and similarity-based reasoning »
Charles Kemp · Patrick Shafto · Allison Berke · Josh Tenenbaum -
2006 Poster: Causal inference in sensorimotor integration »
Konrad P Kording · Josh Tenenbaum -
2006 Tutorial: Bayesian Models of Human Learning and Inference »
Josh Tenenbaum