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Zachary Lee

Publications and source records attributed to Zachary Lee.

8 recordsLinked to original sources

TerraZero: Procedural Driving Simulation for Zero-Demonstration Self-Play at Scale

Training robust autonomous driving agents requires a simulator fast enough for reinforcement learning at scale, realistic enough to ground behavior in real-world map structure, and diverse enough to cover the safety-critical long tail that logged data rarely contains. We present TerraZero, a procedural driving simulator and self-play training stack that meets these goals. A configurable C engine runs simulation on the CPU and policy inference on the GPU over a zero-copy path, sustaining 1.3M agent-steps per second on a single server-grade GPU, far faster than existing object-level simulators, while keeping fidelity lighter single-agent systems omit: heterogeneous agents, multiple dynamics models, and full traffic-rule enforcement. TerraZero uses logged data only as a source of real-world map geometry, populating each map with randomized rule-based road users and signal controllers and randomizing agent dynamics, rewards, and sizes per episode, so one map yields an effectively unbounded set of scenarios. Every reported policy trains from scratch by reinforcement learning alone, with zero human demonstrations, no imitation, no logged trajectories, and no fallback planner at inference, on a compute-efficient self-play recipe scaled across GPUs. The policies generalize zero-shot across cities and datasets, including emergent left-hand-traffic driving without explicit supervision. As an ego policy, a single checkpoint is, to our knowledge, the first fully learned policy to top both val14 and the interactive long-tail InterPlan suite. On Waymo Open Sim Agents realism the same recipe outperforms other demonstration-free methods and is competitive with the strongest reference-anchored self-play method. One stack serves both roles: state-of-the-art demonstration-free driving policies across dynamics for cars and trucks, and sim agents that jointly control vehicles, pedestrians, and cyclists.

cs.LG

PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectives

Recent advances in Gaussian Splatting have enabled fast, high-fidelity 3D scene generation, yet these methods remain purely visual and lack an understanding of how shapes behave in the physical world. We introduce Physics-Guided 3D Gaussian Splatting (PG-3DGS), a framework that couples differentiable physics simulation with 3D Gaussian representations to generate 3D structures satisfying physics functionalities. By allowing physical objectives to guide the shape optimization process alongside visual losses, our approach produces geometries that are not only photometrically accurate but also physically functional. The model learns to adjust shapes so that the generated objects exhibit physically meaningful behaviors, for example, teapots that can pour and airplanes that can generate lift, without sacrificing visual quality. Experiments on pouring and aerodynamic lift tasks show that PG-3DGS improves physical functionality while preserving visual quality. In addition to simulation gains, bench-top physical lift tests with 3D-printed aircraft (Cessna, B-2 Spirit, and paper plane) under identical airflow conditions show higher scale-measured lift for PG-3DGS, generated structures than an appearance-matching baseline in all three cases. Our unified framework connects appearance-based reconstruction with physics-based reasoning, enabling end-to-end generation of 3D structures that both look realistic and function correctly.

cs.CV

Low-regularity invariant measure for the complex-valued mKdV

In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an invariant measure supported at low-regularity. This work complements the work of Kenig et al., which constructed invariant measures supported in higher-regularity spaces for the non-renormalized mKdV. Due to the low-regularity of the support of the measure, we are forced to work in Fourier-Lebesgue spaces. The fact that we consider the complex-valued mKdV makes the problem more complicated than the real-valued case, which was previously considered.

math.AP

An inverse Problem for the cubic $\alpha$-NLS in Sobolev spaces

In this work, we address an inverse problem for a defocusing cubic nonlinear Schr\"{o}dinger (NLS) equation in dimensions $d\in\{1, 2,3\}$ in a range of Sobolev spaces $H^s(\mathbb{R}^d)$ by employing the method of approximate solutions. We recover a smooth, space-dependent and compactly supported function $\alpha$ that controls the nonlinearity (and thus self-interaction strength) in a multiplicative fashion. To the best of our knowledge, this is the first work based on approximate solutions in Sobolev spaces that treats an inverse problem for the NLS and provides explicit recovery of $\alpha$.

math.AP

Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates

In this paper, we show that the one dimensional septic nonlinear Schrödinger equation is globally well-posed and scatters in $H^s (\mathbb{R})$ when $s > 19/54$. We prove new smoothing estimates on the nonlinear Duhamel part of the solution and utilize a linear-nonlinear decomposition to take advantage of the gained regularity. We also prove new $L^{p+3}_{t,x}$ almost Morawetz estimates for the defocusing $p-$NLS adapted to the low-regularity setting, before specializing to the septic case $p=7$.

math.AP

On uniqueness properties of solutions of the generalized fourth-order Schrödinger equations

In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension $d$ of the following forms, $$i \partial_t u + \sum_{j=1}^d \partial_{x_j}^{\, 4} u = V(t, x) u, \quad \text{and} \quad i \partial_t u + \sum_{j=1}^d \partial_{x_j}^{\, 4} u + F (u, \bar{u}) = 0.$$ We show that a linear solution $u$ with fast enough decay in certain Sobolev spaces at two different times has to be trivial. Consequently, if the difference between two nonlinear solutions $u_1$ and $u_2$ decays sufficiently fast at two different times, it implies that $u_1 \equiv u_2$.

math.AP

On recovering the nonlinearity for generalized higher-order Schrödinger equations

In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schrödinger equations to higher-order Schrödinger equations with a more general nonlinearity. More precisely, we consider a spatially-localized nonlinear higher-order Schrödinger equation and recover the spatially-localized coefficient by the solutions with data given by small-amplitude wave packets.

math.AP

Towards Phase Balancing using Energy Storage

Ad-hoc growth of single-phase-connected distributed energy resources, such as solar generation and electric vehicles, can lead to network unbalance with negative consequences on the quality and efficiency of electricity supply. Case-studies are presented for a substation in Madeira, Portugal and an EV charging facility in Pasadena, California. These case studies show that phase imbalance can happen due to a large amount of distributed generation (DG) and electric vehicle (EV) integration. We conducted stylized load-flow analysis on a radial distribution network using an openDSS-based simulator to understand such negative effects of phase imbalance on neutral and phase conductor losses, and in voltage drop/rise. We evaluate the integration of storage in the distribution network as a possible solution for mitigating effects caused by imbalance. We present control architectures of storage operation for phase balancing. Numerically we show that relatively small-sized storage (compared to unbalance magnitude) can significantly reduce network imbalance. We identify the end node of the feeder as the best location to install storage.

eess.SY