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Greg Turk

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Machine Learning Computer Vision Graphics Biological Physics Computational Geometry Robotics

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preprint2026arXiv

Generative Modeling with Orbit-Space Particle Flow Matching

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

preprint2022arXiv

Robot Learning from Randomized Simulations: A Review

The rise of deep learning has caused a paradigm shift in robotics research, favoring methods that require large amounts of data. Unfortunately, it is prohibitively expensive to generate such data sets on a physical platform. Therefore, state-of-the-art approaches learn in simulation where data generation is fast as well as inexpensive and subsequently transfer the knowledge to the real robot (sim-to-real). Despite becoming increasingly realistic, all simulators are by construction based on models, hence inevitably imperfect. This raises the question of how simulators can be modified to facilitate learning robot control policies and overcome the mismatch between simulation and reality, often called the 'reality gap'. We provide a comprehensive review of sim-to-real research for robotics, focusing on a technique named 'domain randomization' which is a method for learning from randomized simulations.

preprint2021arXiv

Learning to Manipulate Amorphous Materials

We present a method of training character manipulation of amorphous materials such as those often used in cooking. Common examples of amorphous materials include granular materials (salt, uncooked rice), fluids (honey), and visco-plastic materials (sticky rice, softened butter). A typical task is to spread a given material out across a flat surface using a tool such as a scraper or knife. We use reinforcement learning to train our controllers to manipulate materials in various ways. The training is performed in a physics simulator that uses position-based dynamics of particles to simulate the materials to be manipulated. The neural network control policy is given observations of the material (e.g. a low-resolution density map), and the policy outputs actions such as rotating and translating the knife. We demonstrate policies that have been successfully trained to carry out the following tasks: spreading, gathering, and flipping. We produce a final animation by using inverse kinematics to guide a character's arm and hand to match the motion of the manipulation tool such as a knife or a frying pan.

preprint2020arXiv

Bodies at Rest: 3D Human Pose and Shape Estimation from a Pressure Image using Synthetic Data

People spend a substantial part of their lives at rest in bed. 3D human pose and shape estimation for this activity would have numerous beneficial applications, yet line-of-sight perception is complicated by occlusion from bedding. Pressure sensing mats are a promising alternative, but training data is challenging to collect at scale. We describe a physics-based method that simulates human bodies at rest in a bed with a pressure sensing mat, and present PressurePose, a synthetic dataset with 206K pressure images with 3D human poses and shapes. We also present PressureNet, a deep learning model that estimates human pose and shape given a pressure image and gender. PressureNet incorporates a pressure map reconstruction (PMR) network that models pressure image generation to promote consistency between estimated 3D body models and pressure image input. In our evaluations, PressureNet performed well with real data from participants in diverse poses, even though it had only been trained with synthetic data. When we ablated the PMR network, performance dropped substantially.

preprint2020arXiv

Learning Novel Policies For Tasks

In this work, we present a reinforcement learning algorithm that can find a variety of policies (novel policies) for a task that is given by a task reward function. Our method does this by creating a second reward function that recognizes previously seen state sequences and rewards those by novelty, which is measured using autoencoders that have been trained on state sequences from previously discovered policies. We present a two-objective update technique for policy gradient algorithms in which each update of the policy is a compromise between improving the task reward and improving the novelty reward. Using this method, we end up with a collection of policies that solves a given task as well as carrying out action sequences that are distinct from one another. We demonstrate this method on maze navigation tasks, a reaching task for a simulated robot arm, and a locomotion task for a hopper. We also demonstrate the effectiveness of our approach on deceptive tasks in which policy gradient methods often get stuck.

preprint2013arXiv

The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion

Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modelling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce "fiber walks" as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modelled as a lateral contraction of the lattice. This contraction influences the possible follow-up steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness.