arXiv subjects

Adam J. Thorpe

Publications and source records attributed to Adam J. Thorpe.

At least 19 recordsLinked to original sources

arXiv2026

Path Planning in Physically Viable World Models

Robots deployed in unstructured outdoor environments often plan from scene reconstructions collected before deployment because operators cannot remap large or remote sites before every mission. As a result, robots must make long-horizon planning decisions using stale maps that assume the terrain remains unchanged, even though physical changes to the environment may render previously feasible routes unsafe or unreachable at execution time. We present a physically viable world model for evaluating what-if queries for robot navigation under future terrain change. The system augments reconstructed 3D Gaussian splat scenes with physics-based simulation to generate physically modified versions of the same environment without recollecting sensor data or rebuilding the map. We then implement a terrain-aware planner that accounts for physical events, obstacles, and deformations that are simulated by the world model. This allows robots and human operators to evaluate whether planned routes remain feasible before committing to a planned route, particularly in constrained environments where retreat or recovery may become impossible once conditions change. We evaluate the system on a real outdoor field site in Central Texas using simulated flooding across multiple severity levels. We measure route and mission feasibility as terrain conditions deteriorate under physically simulated interventions. Our results show that physically viable world models expose long-horizon route failures and rerouting behavior that are not apparent when planning only on the original reconstructed environment, allowing robots to evaluate how future terrain changes may affect route feasibility before deployment.

cs.RO↗

arXiv2026

Physically Viable World Models: A Case for Query-Conditioned Embodied AI

World models for embodied AI must be physically viable: constructed to answer intervention queries by representing the physical structure governing action outcomes, rather than merely predicting future observations. Existing observation-predictive world models can produce visually plausible but physically wrong rollouts. This failure is structural; distinct physical systems can look identical yet diverge under intervention. We expose this problem with controlled benchmarks that fix the visible scene while varying latent physics. We show that such models may recommend infeasible actions, mispredict interaction outcomes, or certify unsafe behavior. We argue that embodied AI requires world models that identify the simplest physical abstraction sufficient to answer an intervention query. Such a model comprises modular components, including environment representation, latent state and parameter estimation, action specification, interventional dynamics, and query-level response. An autonomous orchestrator should identify the relevant abstraction and compose compatible learned and structured components per query. When closed-form physics is unavailable, uncertain, or costly, the transition model may be analytic, simulated, learned, or hybrid, but it must preserve the structure that determines interventional outcomes. This decomposition makes the model interpretable, its components verifiable, and its outputs auditable against the query. It also provides a design principle for new world models and a feasibility test for existing ones: the right abstraction is not the most detailed model of the world, but the simplest model that preserves the distinctions relevant to the query. We demonstrate this approach on queries that existing systems fail to answer correctly, and outline how an orchestrator can dynamically assemble and adapt physically viable models for planning, control, and verification.

cs.AI↗

arXiv2025

Learning Generalizable Neural Operators for Inverse Problems

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that addresses this limitation. Our key innovation is to decouple function representation from the inverse map. We learn neural basis functions for the input and output spaces, then train inverse models that operate on the resulting coefficient space. This structure allows us to learn deterministic, invertible, and probabilistic models within a single framework, and to choose models based on the degree of ill-posedness. We evaluate our approach on six inverse PDE benchmarks, including two novel datasets, and compare against existing invertible neural operator baselines. We learn probabilistic models that capture uncertainty and input variability, and remain robust to measurement noise due to implicit denoising in the coefficient calculation. Our results show consistent re-simulation performance across varying levels of ill-posedness. By separating representation from inversion, our framework enables scalable surrogate models for inverse problems that generalize across instances, domains, and degrees of ill-posedness.

cs.LG↗

arXiv2025

Function Spaces Without Kernels: Learning Compact Hilbert Space Representations

Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning and kernel methods by defining a kernel through an inner product of the learned feature map. This kernel-theoretic perspective explains their ability to scale independently of dataset size while adapting to the intrinsic structure of data, and it enables kernel-style analysis of neural models. Building on this foundation, we develop two training algorithms that learn compact bases: a progressive training approach that constructively grows bases, and a train-then-prune approach that offers a computationally efficient alternative after training. Both approaches use principles from PCA to reveal the intrinsic dimension of the learned space. In parallel, we derive finite-sample generalization bounds using Rademacher complexity and PAC-Bayes techniques, providing inference time guarantees. We validate our approach on a polynomial benchmark with a known intrinsic dimension, and on nonlinear dynamical systems including a Van der Pol oscillator and a two-body orbital model, demonstrating that the same accuracy can be achieved with substantially fewer basis functions. This work suggests a path toward neural predictors with kernel-level guarantees, enabling adaptable models that are both efficient and principled at scale.

cs.LG↗

arXiv2025

Zero to Autonomy in Real-Time: Online Adaptation of Dynamics in Unstructured Environments

Autonomous robots must go from zero prior knowledge to safe control within seconds to operate in unstructured environments. Abrupt terrain changes, such as a sudden transition to ice, create dynamics shifts that can destabilize planners unless the model adapts in real-time. We present a method for online adaptation that combines function encoders with recursive least squares, treating the function encoder coefficients as latent states updated from streaming odometry. This yields constant-time coefficient estimation without gradient-based inner-loop updates, enabling adaptation from only a few seconds of data. We evaluate our approach on a Van der Pol system to highlight algorithmic behavior, in a Unity simulator for high-fidelity off-road navigation, and on a Clearpath Jackal robot, including on a challenging terrain at a local ice rink. Across these settings, our method improves model accuracy and downstream planning, reducing collisions compared to static and meta-learning baselines.

cs.RO↗

arXiv2025

Online Adaptation of Terrain-Aware Dynamics for Planning in Unstructured Environments

Autonomous mobile robots operating in remote, unstructured environments must adapt to new, unpredictable terrains that can change rapidly during operation. In such scenarios, a critical challenge becomes estimating the robot's dynamics on changing terrain in order to enable reliable, accurate navigation and planning. We present a novel online adaptation approach for terrain-aware dynamics modeling and planning using function encoders. Our approach efficiently adapts to new terrains at runtime using limited online data without retraining or fine-tuning. By learning a set of neural network basis functions that span the robot dynamics on diverse terrains, we enable rapid online adaptation to new, unseen terrains and environments as a simple least-squares calculation. We demonstrate our approach for terrain adaptation in a Unity-based robotics simulator and show that the downstream controller has better empirical performance due to higher accuracy of the learned model. This leads to fewer collisions with obstacles while navigating in cluttered environments as compared to a neural ODE baseline.

cs.RO↗

arXiv2025

Function Encoders: A Principled Approach to Transfer Learning in Hilbert Spaces

A central challenge in transfer learning is designing algorithms that can quickly adapt and generalize to new tasks without retraining. Yet, the conditions of when and how algorithms can effectively transfer to new tasks is poorly characterized. We introduce a geometric characterization of transfer in Hilbert spaces and define three types of inductive transfer: interpolation within the convex hull, extrapolation to the linear span, and extrapolation outside the span. We propose a method grounded in the theory of function encoders to achieve all three types of transfer. Specifically, we introduce a novel training scheme for function encoders using least-squares optimization, prove a universal approximation theorem for function encoders, and provide a comprehensive comparison with existing approaches such as transformers and meta-learning on four diverse benchmarks. Our experiments demonstrate that the function encoder outperforms state-of-the-art methods on four benchmark tasks and on all three types of transfer.

cs.LG↗

arXiv2024

Basis-to-Basis Operator Learning Using Function Encoders

We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts: learning sets of basis functions for both the input and output spaces and learning a potentially nonlinear mapping between the coefficients of the basis functions. B2B operator learning circumvents many challenges of prior works, such as requiring data to be at fixed locations, by leveraging classic techniques such as least squares to compute the coefficients. It is especially potent for linear operators, where we compute a mapping between bases as a single matrix transformation with a closed-form solution. Furthermore, with minimal modifications and using the deep theoretical connections between function encoders and functional analysis, we derive operator learning algorithms that are directly analogous to eigen-decomposition and singular value decomposition. We empirically validate B2B operator learning on seven benchmark operator learning tasks and show that it demonstrates a two-orders-of-magnitude improvement in accuracy over existing approaches on several benchmark tasks.

cs.LG↗

arXiv2024

Act Natural! Projecting Autonomous System Trajectories Into Naturalistic Behavior Sets

Autonomous agents operating around human actors must consider how their behaviors might affect those humans, even when not directly interacting with them. To this end, it is often beneficial to be predictable and appear naturalistic. Existing methods to address this problem use human actor intent modeling or imitation learning techniques, but these approaches rarely capture all possible motivations for human behavior or require significant amounts of data. In contrast, we propose a technique for modeling naturalistic behavior as a set of convex hulls computed over a relatively small dataset of human behavior. Given this set, we design an optimization-based filter which projects arbitrary trajectories into it to make them more naturalistic for autonomous agents to execute while also satisfying dynamics constraints. We demonstrate our methods on real-world human driving data from the inD intersection dataset (Bock et al., 2020).

cs.MA↗

arXiv2024

Zero-Shot Transfer of Neural ODEs

Autonomous systems often encounter environments and scenarios beyond the scope of their training data, which underscores a critical challenge: the need to generalize and adapt to unseen scenarios in real time. This challenge necessitates new mathematical and algorithmic tools that enable adaptation and zero-shot transfer. To this end, we leverage the theory of function encoders, which enables zero-shot transfer by combining the flexibility of neural networks with the mathematical principles of Hilbert spaces. Using this theory, we first present a method for learning a space of dynamics spanned by a set of neural ODE basis functions. After training, the proposed approach can rapidly identify dynamics in the learned space using an efficient inner product calculation. Critically, this calculation requires no gradient calculations or retraining during the online phase. This method enables zero-shot transfer for autonomous systems at runtime and opens the door for a new class of adaptable control algorithms. We demonstrate state-of-the-art system modeling accuracy for two MuJoCo robot environments and show that the learned models can be used for more efficient MPC control of a quadrotor.

cs.RO↗

arXiv2024

Sensing Resource Allocation Against Data-Poisoning Attacks in Traffic Routing

Data-poisoning attacks can disrupt the efficient operations of transportation systems by misdirecting traffic flows via falsified data. One challenge in countering these attacks is to reduce the uncertainties on the types of attacks, such as the distribution of their targets and intensities. We introduce a resource allocation method in transportation networks to detect and distinguish different types of attacks and facilitate efficient traffic routing. The idea is to first cluster different types of attacks based on the corresponding optimal routing strategies, then allocate sensing resources to a subset of network links to distinguish attacks from different clusters via lexicographical mixed-integer programming. We illustrate the application of the proposed method using the Anaheim network, a benchmark model in traffic routing that contains more than 400 nodes and 900 links.

math.OC↗

arXiv2024

Active Learning of Dynamics Using Prior Domain Knowledge in the Sampling Process

We present an active learning algorithm for learning dynamics that leverages side information by explicitly incorporating prior domain knowledge into the sampling process. Our proposed algorithm guides the exploration toward regions that demonstrate high empirical discrepancy between the observed data and an imperfect prior model of the dynamics derived from side information. Through numerical experiments, we demonstrate that this strategy explores regions of high discrepancy and accelerates learning while simultaneously reducing model uncertainty. We rigorously prove that our active learning algorithm yields a consistent estimate of the underlying dynamics by providing an explicit rate of convergence for the maximum predictive variance. We demonstrate the efficacy of our approach on an under-actuated pendulum system and on the half-cheetah MuJoCo environment.

eess.SY↗

arXiv2023

Refining Human-Centered Autonomy Using Side Information

Data-driven algorithms for human-centered autonomy use observed data to compute models of human behavior in order to ensure safety, correctness, and to avoid potential errors that arise at runtime. However, such algorithms often neglect useful a priori knowledge, known as side information, that can improve the quality of data-driven models. We identify several key challenges in human-centered autonomy, and identify possible approaches to incorporate side information in data-driven models of human behavior.

cs.HC↗

arXiv2023

Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in real-world scenarios where only limited observations of the system are available. Furthermore, purely data-driven methods often neglect useful a priori knowledge, such as approximate models of the system dynamics. We present a method to incorporate such prior knowledge into data-driven control algorithms using kernel embeddings, a nonparametric machine learning technique based in the theory of reproducing kernel Hilbert spaces. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We formulate the biased learning problem as a least-squares problem with a regularization term that is informed by the dynamics, that has an efficiently computable, closed-form solution. Through numerical experiments, we empirically demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline. We demonstrate an application of our method to control through a target tracking problem with nonholonomic dynamics, and on spring-mass-damper and F-16 aircraft state prediction tasks.

eess.SY↗

arXiv2022

Data-Driven Stochastic Optimal Control Using Kernel Gradients

We present an empirical, gradient-based method for solving data-driven stochastic optimal control problems using the theory of kernel embeddings of distributions. By embedding the integral operator of a stochastic kernel in a reproducing kernel Hilbert space, we can compute an empirical approximation of stochastic optimal control problems, which can then be solved efficiently using the properties of the RKHS. Existing approaches typically rely upon finite control spaces or optimize over policies with finite support to enable optimization. In contrast, our approach uses kernel-based gradients computed using observed data to approximate the cost surface of the optimal control problem, which can then be optimized using gradient descent. We apply our technique to the area of data-driven stochastic optimal control, and demonstrate our proposed approach on a linear regulation problem for comparison and on a nonlinear target tracking problem.

math.OC↗

arXiv2022

Characterizing Within-Driver Variability in Driving Dynamics During Obstacle Avoidance Maneuvers

Variability in human response creates non-trivial challenges for modeling and control of human-automation systems. As autonomy becomes pervasive, methods that can accommodate human variability will become paramount, to ensure efficiency, safety, and high levels of performance. We propose an easily computable modeling framework which takes advantage of a metric to assess variability in individual human response in a dynamic task that subjects repeat over several trials. Our approach is based in a transformation of observed trajectories to a reproducing kernel Hilbert space, which captures variability in human response as a distribution embedded within the Hilbert space. We evaluate the similarity across responses via the maximum mean discrepancy, which measures the distance between distributions within the Hilbert space. We apply this metric to a difficult driving task designed to elucidate differences across subjects. We conducted a pilot study with 6 subjects in an advanced driving simulator, in which subjects were tasked with collision avoidance of an obstacle in the middle of the road, around a blind corner, in a nighttime scenario, while steering only with the non-dominant hand.

eess.SY↗

arXiv2022

SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods

We present SOCKS, a data-driven stochastic optimal control toolbox based in kernel methods. SOCKS is a collection of data-driven algorithms that compute approximate solutions to stochastic optimal control problems with arbitrary cost and constraint functions, including stochastic reachability, which seeks to determine the likelihood that a system will reach a desired target set while respecting a set of pre-defined safety constraints. Our approach relies upon a class of machine learning algorithms based in kernel methods, a nonparametric technique which can be used to represent probability distributions in a high-dimensional space of functions known as a reproducing kernel Hilbert space. As a nonparametric technique, kernel methods are inherently data-driven, meaning that they do not place prior assumptions on the system dynamics or the structure of the uncertainty. This makes the toolbox amenable to a wide variety of systems, including those with nonlinear dynamics, black-box elements, and poorly characterized stochastic disturbances. We present the main features of SOCKS and demonstrate its capabilities on several benchmarks.

cs.LG↗

arXiv2022

Data-Driven Chance Constrained Control using Kernel Distribution Embeddings

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.

eess.SY↗