About

I am interested in the areas of computer graphics, scientific computing, programming languages and robotics. Specifically, I develop numerical methods in computational physics that can benefit from the compute power available on modern workstations, by leveraging accelerations both at the algorithmic and systems level. Recently, we have started applying these techniques for learning unknown physical parameters for motion planning and control in robotics, and for designing correctly-rounded implementations of elementary functions for new floating-point variants. My long term goal is to enable the design of next generation algorithms that can facilitate interdisciplinary collaboration with researchers in engineering and medicine for understanding phenomena that are intractable by current means.

Research topics

• Computer Science
• Mathematics
• Mathematical optimization
• Artificial Intelligence
• Physics
• Mechanics
• Mathematical analysis
• Applied mathematics
• Algorithm
• Pure mathematics

Selected publications

• An Open-Source, Reproducible Tensegrity Robot That Can Navigate Among Obstacles

  IEEE Robotics and Automation Letters · 2026-04-06 · 1 citations

  article

  Tensegrity robots, composed of rigid struts and elastic tendons, provide impact resistance, low mass, and adaptability to unstructured terrain. Their compliance and complex, coupled dynamics, however, present modeling and control challenges, hindering planning and obstacle avoidance. This paper presents a complete, open-source, and reproducible system that enables navigation for a 3-bar tensegrity robot. The system comprises: (i) an inexpensive, open-source hardware design, and (ii) an integrated, open-source software stack for physics-based modeling, system identification, state estimation, path planning, and control. All hardware and software are publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://tensegrity.yale.edu/</uri> tensegrity.yale.edu. The proposed system tracks the robot using a static overhead camera and executes collision-free paths to a goal among known obstacle locations. System robustness is demonstrated through experiments involving unmodeled environmental challenges, including a vertical drop, an incline, and granular media, culminating in an outdoor field demonstration. To validate reproducibility, experiments were conducted using robot instances at two different laboratories. This work provides the robotics community with a complete navigation system for a compliant, impact-resistant, and shape-morphing robot. This system is intended to serve as a springboard for advancing the navigation capabilities of other unconventional robotic platforms.

  PublisherDOI

• CableRobotGraphSim: A Graph Neural Network for Modeling Partially Observable Cable-Driven Robot Dynamics

  Open MIND · 2026-02-24

  preprintSenior author

  General-purpose simulators have accelerated the development of robots. Traditional simulators based on first-principles, however, typically require full-state observability or depend on parameter search for system identification. This work presents \texttt{CableRobotGraphSim}, a novel Graph Neural Network (GNN) model for cable-driven robots that aims to address shortcomings of prior simulation solutions. By representing cable-driven robots as graphs, with the rigid-bodies as nodes and the cables and contacts as edges, this model can quickly and accurately match the properties of other simulation models and real robots, while ingesting only partially observable inputs. Accompanying the GNN model is a sim-and-real co-training procedure that promotes generalization and robustness to noisy real data. This model is further integrated with a Model Predictive Path Integral (MPPI) controller for closed-loop navigation, which showcases the model's speed and accuracy.

  DOI

• CableRobotGraphSim: A Graph Neural Network for Modeling Partially Observable Cable-Driven Robot Dynamics

  ArXiv.org · 2026-02-24

  articleOpen accessSenior author

  General-purpose simulators have accelerated the development of robots. Traditional simulators based on first-principles, however, typically require full-state observability or depend on parameter search for system identification. This work presents \texttt{CableRobotGraphSim}, a novel Graph Neural Network (GNN) model for cable-driven robots that aims to address shortcomings of prior simulation solutions. By representing cable-driven robots as graphs, with the rigid-bodies as nodes and the cables and contacts as edges, this model can quickly and accurately match the properties of other simulation models and real robots, while ingesting only partially observable inputs. Accompanying the GNN model is a sim-and-real co-training procedure that promotes generalization and robustness to noisy real data. This model is further integrated with a Model Predictive Path Integral (MPPI) controller for closed-loop navigation, which showcases the model's speed and accuracy.

  PublisherOA PDF

• A Closest Point Method for PDEs on Manifolds with Interior Boundary Conditions for Geometry Processing

  ACM Transactions on Graphics · 2024-06-17 · 6 citations

  articleOpen access

  Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in ℝ 2 or ℝ 3 , such as curves or surfaces. Such manifold PDEs often involve boundary conditions (e.g., Dirichlet or Neumann) prescribed at points or curves on the manifold’s interior or along the geometric (exterior) boundary of an open manifold. However, input manifolds can take many forms (e.g., triangle meshes, parametrizations, point clouds, implicit functions, etc.). Typically, one must generate a mesh to apply finite element-type techniques or derive specialized discretization procedures for each distinct manifold representation. We propose instead to address such problems in a unified manner through a novel extension of the closest point method (CPM) to handle interior boundary conditions. CPM solves the manifold PDE by solving a volumetric PDE defined over the Cartesian embedding space containing the manifold and requires only a closest point representation of the manifold. Hence, CPM supports objects that are open or closed, orientable or not, and of any codimension. To enable support for interior boundary conditions, we derive a method that implicitly partitions the embedding space across interior boundaries. CPM’s finite difference and interpolation stencils are adapted to respect this partition while preserving second-order accuracy. Additionally, we develop an efficient sparse-grid implementation and numerical solver that can scale to tens of millions of degrees of freedom, allowing PDEs to be solved on more complex manifolds. We demonstrate our method’s convergence behavior on selected model PDEs and explore several geometry processing problems: diffusion curves on surfaces, geodesic distance, tangent vector field design, harmonic map construction, and reaction-diffusion textures. Our proposed approach thus offers a powerful and flexible new tool for a range of geometry processing tasks on general manifold representations.

  PublisherOA PDFDOI

• Learning Differentiable Tensegrity Dynamics using Graph Neural Networks

  arXiv (Cornell University) · 2024-10-16

  preprintOpen accessSenior author

  Tensegrity robots are composed of rigid struts and flexible cables. They constitute an emerging class of hybrid rigid-soft robotic systems and are promising systems for a wide array of applications, ranging from locomotion to assembly. They are difficult to control and model accurately, however, due to their compliance and high number of degrees of freedom. To address this issue, prior work has introduced a differentiable physics engine designed for tensegrity robots based on first principles. In contrast, this work proposes the use of graph neural networks to model contact dynamics over a graph representation of tensegrity robots, which leverages their natural graph-like cable connectivity between end caps of rigid rods. This learned simulator can accurately model 3-bar and 6-bar tensegrity robot dynamics in simulation-to-simulation experiments where MuJoCo is used as the ground truth. It can also achieve higher accuracy than the previous differentiable engine for a real 3-bar tensegrity robot, for which the robot state is only partially observable. When compared against direct applications of recent mesh-based graph neural network simulators, the proposed approach is computationally more efficient, both for training and inference, while achieving higher accuracy. Code and data are available at https://github.com/nchen9191/tensegrity_gnn_simulator_public

  PublisherOA PDFDOI

• Spectral reordering for faster elasticity simulations

  The Visual Computer · 2024-06-18

  articleOpen accessSenior author

  Abstract We present a novel method for faster physics simulations of elastic solids. Our key idea is to reorder the unknown variables according to the Fiedler vector (i.e., the second-smallest eigenvector) of the combinatorial Laplacian. It is well known in the geometry processing community that the Fiedler vector brings together vertices that are geometrically nearby, causing fewer cache misses when computing differential operators. However, to the best of our knowledge, this idea has not been exploited to accelerate simulations of elastic solids which require an expensive linear (or non-linear) system solve at every time step. The cost of computing the Fiedler vector is negligible, thanks to an algebraic Multigrid-preconditioned Conjugate Gradients (AMGPCG) solver. We observe that our AMGPCG solver requires approximately 1 s for computing the Fiedler vector for a mesh with approximately 50 K vertices or 100 K tetrahedra. Our method provides a speed-up between $$10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>10</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> – $$30\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>30</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> at every time step, which can lead to considerable savings, noting that even modest simulations of elastic solids require at least 240 time steps. Our method is easy to implement and can be used as a plugin for speeding up existing physics simulators for elastic solids, as we demonstrate through our experiments using the Vega library and the ADMM solver, which use different algorithms for elasticity.

  PublisherOA PDFDOI

• Maximum Consensus Floating Point Solutions for Infeasible Low-Dimensional Linear Programs with Convex Hull as the Intermediate Representation

  Proceedings of the ACM on Programming Languages · 2024-06-20 · 1 citations

  articleOpen access1st authorCorresponding

  This paper proposes a novel method to efficiently solve infeasible low-dimensional linear programs (LDLPs) with billions of constraints and a small number of unknown variables, where all the constraints cannot be satisfied simultaneously. We focus on infeasible linear programs generated in the RL ibm project for creating correctly rounded math libraries. Specifically, we are interested in generating a floating point solution that satisfies the maximum number of constraints. None of the existing methods can solve such large linear programs while producing floating point solutions. We observe that the convex hull can serve as an intermediate representation (IR) for solving infeasible LDLPs using the geometric duality between linear programs and convex hulls. Specifically, some of the constraints that correspond to points on the convex hull are precisely those constraints that make the linear program infeasible. Our key idea is to split the entire set of constraints into two subsets using the convex hull IR: (a) a set <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">X</mml:mi> </mml:math> of feasible constraints and (b) a superset <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">V</mml:mi> </mml:math> of infeasible constraints. Using the special structure of the RL ibm constraints and the presence of a method to check whether a system is feasible or not. we identify a superset of infeasible constraints by computing the convex hull in 2-dimensions. Subsequently, we identify the key constraints (i.e., basis constraints) in the set of feasible constraints <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">X</mml:mi> </mml:math> and use them to create a new linear program whose solution identifies the maximum set of constraints satisfiable in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">V</mml:mi> </mml:math> while satisfying all the constraints in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">X</mml:mi> </mml:math> . This new solver enabled us to improve the performance of the resulting RL ibm polynomials while solving the corresponding linear programs significantly faster.

  PublisherOA PDFDOI

• An Interactive Framework for Visually Realistic 3D Motion Synthesis using Evolutionarily-trained Spiking Neural Networks

  Proceedings of the ACM on Computer Graphics and Interactive Techniques · 2023-05-12 · 1 citations

  article

  We present an end-to-end method for capturing the dynamics of 3D human characters and translating them for synthesizing new, visually-realistic motion sequences. Conventional methods employ sophisticated, but generic, control approaches for driving the joints of articulated characters, paying little attention to the distinct dynamics of human joint movements. In contrast, our approach attempts to synthesize human-like joint movements by exploiting a biologically-plausible, compact network of spiking neurons that drive joint control in primates and rodents. We adapt the controller architecture by introducing learnable components and propose an evolutionary algorithm for training the spiking neural network architectures and capturing diverse joint dynamics. Our method requires only a few samples for capturing the dynamic properties of a joint's motion and exploits the biologically-inspired, trained controller for its reconstruction. More importantly, it can transfer the captured dynamics to new visually-plausible motion sequences. To enable user-dependent tailoring of the resulting motion sequences, we develop an interactive framework that allows for editing and real-time visualization of the controlled 3D character. We also demonstrate the applicability of our method to real human motion capture data by learning the hand joint dynamics from a gesture dataset and using our framework to reconstruct the gestures with our 3D animated character. The compact architecture of our joint controller emerging from its biologically-realistic design, and the inherent capacity of our evolutionary learning algorithm for parallelization, suggest that our approach could provide an efficient and scalable alternative for synthesizing 3D character animations with diverse and visually-realistic motion dynamics.

  PublisherDOI

• A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics

  Proceedings of the ACM on Computer Graphics and Interactive Techniques · 2023-08-16 · 6 citations

  articleSenior author

  We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

  PublisherDOI

• Fast Polynomial Evaluation for Correctly Rounded Elementary Functions using the RLIBM Approach

  2023-02-17 · 5 citations

  article1st authorCorresponding

  This paper proposes fast polynomial evaluation methods for correctly rounded elementary functions generated using our RLibm approach. The resulting functions produce correct results for all inputs with multiple representations and rounding modes. Given an oracle, the RLibm approach approximates the correctly rounded result rather than the real value of an elementary function. A key observation is that there is an interval of real values around the correctly rounded result such that any real value in it rounds to the correct result. This interval is the maximum freedom available to RLibm’s polynomial generation procedure. Subsequently, the problem of generating correctly rounded elementary functions using these intervals can be structured as a linear programming problem. Our prior work on the RLibm approach uses Horner’s method for polynomial evaluation.

  PublisherDOI

Recent grants

• CAREER: Modeling and Simulating Generalized Diffusion for Computer Graphics and Computational Science

  NSF · $500k · 2023–2028

Frequent coauthors

• Kostas E. Bekris

  12 shared

• Santosh Nagarakatte

  Rutgers, The State University of New Jersey

  10 shared

• Kun Wang

  10 shared

• Haozhe Su

  8 shared

• Jay P. Lim

  Rutgers, The State University of New Jersey

  8 shared

• Chengguizi Han

  Rutgers Sexual and Reproductive Health and Rights

  8 shared

• Eftychios Sifakis

  6 shared

• Tao Xue

  6 shared

Labs

• Laboratory for Interactive Virtual Environments (LIVE)PI

Education

• B.S., Computer Science and Engineering

  Indian Institute of Technology Kharagpur

  2008

• Ph.D., Computer Science

  Stanford University

  2013

• Other

  University of Wisconsin-Madison

Awards & honors

• Ralph E. Powe Junior Faculty Enhancement Award 2019
• NSF CAREER Award 2023