arXiv subjects

David Millard

Publications and source records attributed to David Millard.

16 recordsLinked to original sources

arXiv2026

Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting

Machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms, such as advection, diffusive mixing, thermodynamic processes, and forcing, are represented implicitly within a single large neural network. This is particularly problematic for advection, where long-range transport typically requires expensive global interaction mechanisms or deep stacks of local convolutional layers. To address this limitation, we introduce a physics-inspired neural architecture that decomposes latent-state evolution into dedicated advection, diffusion, and reaction operators. Its central component is a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable interpolation on the sphere, allowing the network to learn both a compressed set of latent modes to be transported and their characteristic trajectories. The atmospheric state is projected into latent space and spatially coarsened to a processor grid, where advection, diffusion, and reaction operators jointly evolve the representation. Diffusive mixing and unresolved dissipation are represented by depthwise-separable spatial mixing, while local source terms and vertical interactions are handled through pointwise channel interactions. We evaluate a reference implementation of the proposed architecture on global weather forecasting. Evaluated on ERA5 benchmarks, the reference model achieves competitive deterministic forecast skill, with particularly strong performance at short to medium lead times, while preserving improved spectral fidelity and forecast activity relative to several leading data-driven baselines.

cs.LG↗

arXiv2026

Stability of the Monge Map in Semi-Dual Optimal Transport

This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and sufficient conditions for the convergence of Monge maps without requiring optimality of the dual potential. This analysis helps explain why, in practice, numerical algorithms often require more iterations to update the transport map than the potential.

math.OC↗

arXiv2026

Federated Distributional Reinforcement Learning with Distributional Critic Regularization

Federated reinforcement learning typically aggregates value functions or policies by parameter averaging, which emphasizes expected return and can obscure statistical multimodality and tail behavior that matter in safety-critical settings. We formalize federated distributional reinforcement learning (FedDistRL), where clients parametrize quantile value function critics and federate these networks only. We also propose TR-FedDistRL, which builds a per client, risk-aware Wasserstein barycenter over a temporal buffer. This local barycenter provides a reference region to constrain the parameter averaged critic, ensuring necessary distributional information is not averaged out during the federation process. The distributional trust region is implemented as a shrink-squash step around this reference. Under fixed-policy evaluation, the feasibility map is nonexpansive and the update is contractive in a probe-set Wasserstein metric under evaluation. Experiments on a bandit, multi-agent gridworld, and continuous highway environment show reduced mean-smearing, improved safety proxies (catastrophe/accident rate), and lower critic/policy drift versus mean-oriented and non-federated baselines.

cs.LG↗

arXiv2026

Can Optimal Transport Improve Federated Inverse Reinforcement Learning?

In robotics and multi-agent systems, fleets of autonomous agents often operate in subtly different environments while pursuing a common high-level objective. Directly pooling their data to learn a shared reward function is typically impractical due to differences in dynamics, privacy constraints, and limited communication bandwidth. This paper introduces an optimal transport-based approach to federated inverse reinforcement learning (IRL). Each client first performs lightweight Maximum Entropy IRL locally, adhering to its computational and privacy limitations. The resulting reward functions are then fused via a Wasserstein barycenter, which considers their underlying geometric structure. We further prove that this barycentric fusion yields a more faithful global reward estimate than conventional parameter averaging methods in federated learning. Overall, this work provides a principled and communication-efficient framework for deriving a shared reward that generalizes across heterogeneous agents and environments.

cs.LG↗

arXiv2025

Split Conformal Prediction in the Function Space with Neural Operators

Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample guarantees in finite-dimensional spaces, it does not directly extend to function-valued outputs. Existing approaches (Gaussian processes, Bayesian neural networks, and quantile-based operators) require strong distributional assumptions or yield conservative coverage. This work extends split conformal prediction to function spaces following a two step method. We first establish finite-sample coverage guarantees in a finite-dimensional space using a discretization map in the output function space. Then these guarantees are lifted to the function-space by considering the asymptotic convergence as the discretization is refined. To characterize the effect of resolution, we decompose the conformal radius into discretization, calibration, and misspecification components. This decomposition motivates a regression-based correction to transfer calibration across resolutions. Additionally, we propose two diagnostic metrics (conformal ensemble score and internal agreement) to quantify forecast degradation in autoregressive settings. Empirical results show that our method maintains calibrated coverage with less variation under resolution shifts and achieves better coverage in super-resolution tasks.

cs.LG↗

arXiv2025

DEF: Diffusion-augmented Ensemble Forecasting

We present DEF (\textbf{\ul{D}}iffusion-augmented \textbf{\ul{E}}nsemble \textbf{\ul{F}}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily designed for numerical weather prediction (NWP) solvers, limiting their applicability in the rapidly growing field of machine learning for weather prediction. Consequently, stochastic models in this domain are often developed on a case-by-case basis. We demonstrate that a simple conditional diffusion model can (1) generate meaningful structured perturbations, (2) be applied iteratively, and (3) utilize a guidance term to intuitivey control the level of perturbation. This method enables the transformation of any deterministic neural forecasting system into a stochastic one. With our stochastic extended systems, we show that the model accumulates less error over long-term forecasts while producing meaningful forecast distributions. We validate our approach on the 5.625$^\circ$ ERA5 reanalysis dataset, which comprises atmospheric and surface variables over a discretized global grid, spanning from the 1960s to the present. On this dataset, our method demonstrates improved predictive performance along with reasonable spread estimates.

cs.LG↗

arXiv2025

PEARL: Preconditioner Enhancement through Actor-critic Reinforcement Learning

We present PEARL (Preconditioner Enhancement through Actor-critic Reinforcement Learning), a novel approach to learning matrix preconditioners. Existing preconditioners such as Jacobi, Incomplete LU, and Algebraic Multigrid methods offer problem-specific advantages but rely heavily on hyperparameter tuning. Recent advances have explored using deep neural networks to learn preconditioners, though challenges such as misbehaved objective functions and costly training procedures remain. PEARL introduces a reinforcement learning approach for learning preconditioners, specifically, a contextual bandit formulation. The framework utilizes an actor-critic model, where the actor generates the incomplete Cholesky decomposition of preconditioners, and the critic evaluates them based on reward-specific feedback. To further guide the training, we design a dual-objective function, combining updates from the critic and condition number. PEARL contributes a generalizable preconditioner learning method, dynamic sparsity exploration, and cosine schedulers for improved stability and exploratory power. We compare our approach to traditional and neural preconditioners, demonstrating improved flexibility and iterative solving speed.

cs.LG↗

arXiv2024

Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their underlying dynamics difficult to understand and explain. This paper proposes methodologies to estimate the Koopman operator, providing a linear representation of complex nonlinear dynamics to enhance the transparency of data-driven models. Despite its potential, applying the Koopman operator to large-scale problems, such as atmospheric modeling, remains challenging. This study aims to identify the limitations of existing methods, refine these models to overcome various bottlenecks, and introduce novel convolutional neural network architectures that capture simplified dynamics.

cs.LG↗

arXiv2024

CppFlow: Generative Inverse Kinematics for Efficient and Robust Cartesian Path Planning

In this work we present CppFlow - a novel and performant planner for the Cartesian Path Planning problem, which finds valid trajectories up to 129x faster than current methods, while also succeeding on more difficult problems where others fail. At the core of the proposed algorithm is the use of a learned, generative Inverse Kinematics solver, which is able to efficiently produce promising entire candidate solution trajectories on the GPU. Precise, valid solutions are then found through classical approaches such as differentiable programming, global search, and optimization. In combining approaches from these two paradigms we get the best of both worlds - efficient approximate solutions from generative AI which are made exact using the guarantees of traditional planning and optimization. We evaluate our system against other state of the art methods on a set of established baselines as well as new ones introduced in this work and find that our method significantly outperforms others in terms of the time to find a valid solution and planning success rate, and performs comparably in terms of trajectory length over time. The work is made open source and available for use upon acceptance.

cs.RO↗

arXiv2023

Granular Gym: High Performance Simulation for Robotic Tasks with Granular Materials

Granular materials are of critical interest to many robotic tasks in planetary science, construction, and manufacturing. However, the dynamics of granular materials are complex and often computationally very expensive to simulate. We propose a set of methodologies and a system for the fast simulation of granular materials on Graphics Processing Units (GPUs), and show that this simulation is fast enough for basic training with Reinforcement Learning algorithms, which currently require many dynamics samples to achieve acceptable performance. Our method models granular material dynamics using implicit timestepping methods for multibody rigid contacts, as well as algorithmic techniques for efficient parallel collision detection between pairs of particles and between particle and arbitrarily shaped rigid bodies, and programming techniques for minimizing warp divergence on Single-Instruction, Multiple-Thread (SIMT) chip architectures. We showcase our simulation system on several environments targeted toward robotic tasks, and release our simulator as an open-source tool.

cs.RO↗

arXiv2022

Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulation

To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through a Bayesian inference approach that approximates a posterior distribution over simulation parameters given real sensor measurements. By extending the commonly used Gaussian likelihood model for trajectories via the multiple-shooting formulation, our chosen particle-based inference algorithm Stein Variational Gradient Descent is able to identify highly nonlinear, underactuated systems. We leverage GPU code generation and differentiable simulation to evaluate the likelihood and its gradient for many particles in parallel. Our algorithm infers non-parametric distributions over simulation parameters more accurately than comparable baselines and handles constraints over parameters efficiently through gradient-based optimization. We evaluate estimation performance on several physical experiments. On an underactuated mechanism where a 7-DOF robot arm excites an object with an unknown mass configuration, we demonstrate how our inference technique can identify symmetries between the parameters and provide highly accurate predictions. Project website: https://uscresl.github.io/prob-diff-sim

cs.RO↗

arXiv2021

NeuralSim: Augmenting Differentiable Simulators with Neural Networks

Differentiable simulators provide an avenue for closing the sim-to-real gap by enabling the use of efficient, gradient-based optimization algorithms to find the simulation parameters that best fit the observed sensor readings. Nonetheless, these analytical models can only predict the dynamical behavior of systems for which they have been designed. In this work, we study the augmentation of a novel differentiable rigid-body physics engine via neural networks that is able to learn nonlinear relationships between dynamic quantities and can thus learn effects not accounted for in traditional simulators.Such augmentations require less data to train and generalize better compared to entirely data-driven models. Through extensive experiments, we demonstrate the ability of our hybrid simulator to learn complex dynamics involving frictional contacts from real data, as well as match known models of viscous friction, and present an approach for automatically discovering useful augmentations. We show that, besides benefiting dynamics modeling, inserting neural networks can accelerate model-based control architectures. We observe a ten-fold speed-up when replacing the QP solver inside a model-predictive gait controller for quadruped robots with a neural network, allowing us to significantly improve control delays as we demonstrate in real-hardware experiments. We publish code, additional results and videos from our experiments on our project webpage at https://sites.google.com/usc.edu/neuralsim.

cs.RO↗

arXiv2020

Domain Adversarial Neural Networks for Dysarthric Speech Recognition

Speech recognition systems have improved dramatically over the last few years, however, their performance is significantly degraded for the cases of accented or impaired speech. This work explores domain adversarial neural networks (DANN) for speaker-independent speech recognition on the UAS dataset of dysarthric speech. The classification task on 10 spoken digits is performed using an end-to-end CNN taking raw audio as input. The results are compared to a speaker-adaptive (SA) model as well as speaker-dependent (SD) and multi-task learning models (MTL). The experiments conducted in this paper show that DANN achieves an absolute recognition rate of 74.91% and outperforms the baseline by 12.18%. Additionally, the DANN model achieves comparable results to the SA model's recognition rate of 77.65%. We also observe that when labelled dysarthric speech data is available DANN and MTL perform similarly, but when they are not DANN performs better than MTL.

cs.SD↗

arXiv2020

Augmenting Differentiable Simulators with Neural Networks to Close the Sim2Real Gap

We present a differentiable simulation architecture for articulated rigid-body dynamics that enables the augmentation of analytical models with neural networks at any point of the computation. Through gradient-based optimization, identification of the simulation parameters and network weights is performed efficiently in preliminary experiments on a real-world dataset and in sim2sim transfer applications, while poor local optima are overcome through a random search approach.

cs.RO↗

arXiv2020

Interactive Differentiable Simulation

Intelligent agents need a physical understanding of the world to predict the impact of their actions in the future. While learning-based models of the environment dynamics have contributed to significant improvements in sample efficiency compared to model-free reinforcement learning algorithms, they typically fail to generalize to system states beyond the training data, while often grounding their predictions on non-interpretable latent variables. We introduce Interactive Differentiable Simulation (IDS), a differentiable physics engine, that allows for efficient, accurate inference of physical properties of rigid-body systems. Integrated into deep learning architectures, our model is able to accomplish system identification using visual input, leading to an interpretable model of the world whose parameters have physical meaning. We present experiments showing automatic task-based robot design and parameter estimation for nonlinear dynamical systems by automatically calculating gradients in IDS. When integrated into an adaptive model-predictive control algorithm, our approach exhibits orders of magnitude improvements in sample efficiency over model-free reinforcement learning algorithms on challenging nonlinear control domains.

cs.LG↗

arXiv2020

Automatic Differentiation and Continuous Sensitivity Analysis of Rigid Body Dynamics

A key ingredient to achieving intelligent behavior is physical understanding that equips robots with the ability to reason about the effects of their actions in a dynamic environment. Several methods have been proposed to learn dynamics models from data that inform model-based control algorithms. While such learning-based approaches can model locally observed behaviors, they fail to generalize to more complex dynamics and under long time horizons. In this work, we introduce a differentiable physics simulator for rigid body dynamics. Leveraging various techniques for differential equation integration and gradient calculation, we compare different methods for parameter estimation that allow us to infer the simulation parameters that are relevant to estimation and control of physical systems. In the context of trajectory optimization, we introduce a closed-loop model-predictive control algorithm that infers the simulation parameters through experience while achieving cost-minimizing performance.

cs.RO↗