arXiv subjects

Yorie Nakahira

Publications and source records attributed to Yorie Nakahira.

At least 19 recordsLinked to original sources

arXiv2026

Full-Covariance Smoothing of Bayesian Neural Networks for Online Adaptation

A neural network's layers can be treated as time steps of a state-space model, turning Bayesian training into a smoothing problem: a forward pass propagates Gaussian moments through the network, and a backward Rauch--Tung--Striebel pass updates the weight posteriors in closed form. Such methods learn from each observation in a single pass, in an uncertainty-aware manner, and without gradient-based iterations or replay, which makes them well suited for online adaptation and data-efficient learning. Existing smoothing-based methods, however, are restricted to diagonal covariances across activations, discarding correlations between neurons. We overcome this limitation via a cross-covariance identity that enables full-covariance propagation through a network's nonlinear activations. We derive a one-step-per-layer smoother that approximates as Gaussian only each layer's affine output, and that applies both to deterministic systems with noisy observations and to stochastic systems described by output statistics. We demonstrate this method in non-stationary classification, online dynamics learning, and policy adaptation of a vision-language-action model, and find that it is generally more accurate than other smoothing-based methods.

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arXiv2026

Learning Fractional-Order Dynamics from a Single Trajectory

Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone. This paper studies system identification for discrete-time fractional-order linear time-invariant systems from a single observed trajectory of length $t$, a setting that captures such non-Markovian dynamics through the Grünwald--Letnikov difference operator. Unlike Markovian systems, fractional-order systems couple estimation across the entire history, making both statistical analysis and practical identification more challenging. We propose \emph{Fractional-Order Ordinary-Least-Squares Grid-Search (FO-GS)}, a simple two-stage estimator that exploits the diagonal structure of the fractional-difference operator to decouple the identification problem row-wise. Under the stability assumption, we establish high-probability, non-asymptotic error bounds for estimating both the fractional order and the system matrix in the heterogeneous setting, with both estimation errors scaling as $\mathcal{O}(t^{-1/2})$. Through experiments, we show that \emph{FO-GS} outperforms existing baselines in recovering both the fractional order and the underlying system dynamics.

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arXiv2026

Physics-informed Reinforcement Learning for Stochastic Reach-Avoid Analysis

Stochastic reach-avoid analysis of controlled dynamical systems is an important tool for safety-critical control under uncertainty, in which the reach-avoid probability is characterized by a Hamilton-Jacobi partial differential equation (PDE). However, solving this PDE using conventional numerical methods becomes computationally intractable as the system dimension increases. Physics-informed neural networks (PINNs) may converge to inaccurate local minima when trained primarily through PDE-residual minimization. Reinforcement learning (RL) offers a scalable alternative, but its learned value functions may be inaccurate or inconsistent with the governing PDE. This paper proposes a physics-informed RL (PIRL) framework that combines the complementary strengths of PINNs and RL for stochastic reach-avoid analysis. We develop a scheduled PIRL algorithm in which temporal-difference actor-critic learning first guides the critic toward a meaningful approximation of the reach-avoid value function. PDE-residual and boundary-condition losses are then introduced progressively to enforce consistency with the governing PDE and its boundary conditions. The proposed method mitigates the failure modes of conventional PINN techniques while achieving accuracy comparable to that of successfully trained PINNs. The effectiveness of the proposed framework is demonstrated through two case studies.

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arXiv2026

Online Adaptive Probabilistic Safety Certificate with Language Guidance

Achieving long-term safety in uncertain/extreme environments while accounting for human preferences remains a fundamental challenge for autonomous systems. Existing methods often trade off long-term guarantees for fast real-time control and cannot adapt to variability in human preferences or risk tolerance. To address these limitations, we propose a language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences. The proposed framework integrates natural-language inputs from users and Bayesian estimators of the environment into adaptive safety certificates that explicitly account for user preferences, system dynamics, and quantified uncertainties. Our key technical innovation leverages probabilistic invariance--a generalization of forward invariance to a probability space--to obtain myopic safety conditions with long-term safety guarantees. We validate the framework through numerical simulations of autonomous lane-keeping with human-in-the-loop guidance under uncertain and extreme road conditions, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences. Code is available at https://github.com/hoshino06/adaptive_lane_keeping.

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arXiv2026

Online Safety Filter for Deformable Object Manipulation with Horizon Agnostic Neural Operators

Safety critical control of robotic manipulation tasks involving deformable media such as fluids, cloth, and soft objects remains challenging because existing learning based approaches encode safety indirectly through reward shaping, which provides no guarantee of constraint satisfaction at deployment. We present a constraint driven online safety filter for deformable object manipulation that enforces explicit task level safety constraints in real time by minimally modifying any nominal control policy. Our approach combines two key components: a horizon agnostic neural operator that learns the boundary input output mapping of the underlying PDE dynamics and generalizes across variable rollout lengths without retraining, and a boundary control barrier function that certifies safety at the task relevant output level via a lightweight quadratic program. The resulting safety constraint is affine in the boundary input rate, enabling real time online filtering. We evaluate the proposed method on fluid manipulation tasks in FluidLab, where the filter improves safe trajectory rates by up to 22% over unfiltered base policies while also reducing the number of steps required to reach the safe set, demonstrating that constraint driven safety enforcement is both more reliable and more efficient than reward shaping approaches.

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arXiv2026

OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference

Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving PDEs across heterogeneous settings remains challenging. Prior work on LLM-based code generation and transformer-based foundation models for PDE learning has shown promising advances. However, a persistent trade-off between execution success rate and numerical accuracy arises, particularly when generalization to unseen parameters and boundary conditions is required. In this work, we propose OpInf-LLM, an LLM parametric PDE solving framework via operator inference. The proposed framework leverages small amounts of solution data to enable accurate prediction of diverse PDE instances, including unseen parameters and configurations, and provides seamless integration with LLMs for natural language task specification and physics-based reasoning of proper feature parameterization. Its low computational demands and unified solution pipeline further enable a high execution success rate across heterogeneous settings, opening new possibilities for generalizable reduced-order modeling in LLM-based PDE solving.

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arXiv2026

Fractional Risk Analysis of Stochastic Systems with Jumps and Memory

Accurate risk assessment is essential for safety-critical autonomous and control systems under uncertainty. In many real-world settings, stochastic dynamics exhibit asymmetric jumps and long-range memory, making long-term risk probabilities difficult to estimate across varying system dynamics, initial conditions, and time horizons. Existing sampling-based methods are computationally expensive due to repeated long-horizon simulations to capture rare events, while existing partial differential equation (PDE)-based formulations are largely limited to Gaussian or symmetric jump dynamics and typically treat memory effects in isolation. In this paper, we address these challenges by deriving a space- and time-fractional PDE that characterizes long-term safety and recovery probabilities for stochastic systems with both asymmetric Levy jumps and memory. This unified formulation captures nonlocal spatial effects and temporal memory within a single framework and enables the joint evaluation of risk across initial states and horizons. We show that the proposed PDE accurately characterizes long-term risk and reveals behaviors that differ fundamentally from systems without jumps or memory and from standard non-fractional PDEs. Building on this characterization, we further demonstrate how physics-informed learning can efficiently solve the fractional PDEs, enabling accurate risk prediction across diverse configurations and strong generalization to out-of-distribution dynamics.

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arXiv2026

Physics-Informed Deep B-Spline Networks

Physics-informed machine learning offers a promising framework for solving complex partial differential equations (PDEs) by integrating observational data with governing physical laws. However, learning PDEs with varying parameters and changing initial conditions and boundary conditions (ICBCs) with theoretical guarantees remains an open challenge. In this paper, we propose physics-informed deep B-spline networks, a novel technique that approximates a family of PDEs with different parameters and ICBCs by learning B-spline control points through neural networks. The proposed B-spline representation reduces the learning task from predicting solution values over the entire domain to learning a compact set of control points, enforces strict compliance to initial and Dirichlet boundary conditions by construction, and enables analytical computation of derivatives for incorporating PDE residual losses. While existing approximation and generalization theories are not applicable in this setting - where solutions of parametrized PDE families are represented via B-spline bases - we fill this gap by showing that B-spline networks are universal approximators for such families under mild conditions. We also derive generalization error bounds for physics-informed learning in both elliptic and parabolic PDE settings, establishing new theoretical guarantees. Finally, we demonstrate in experiments that the proposed technique has improved efficiency-accuracy tradeoffs compared to existing techniques in a dynamical system problem with discontinuous ICBCs and can handle nonhomogeneous ICBCs and non-rectangular domains.

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arXiv2026

Multi-Level Multi-Fidelity Methods for Path Integral and Safe Control

Sampling-based approaches are widely used in systems without analytic models to estimate risk or find optimal control. However, gathering sufficient data in such scenarios can be prohibitively costly. On the other hand, in many situations, low-fidelity models or simulators are available from which samples can be obtained at low cost. In this paper, we propose an efficient approach for risk quantification and path integral control that leverages such data from multiple models with heterogeneous sampling costs. A key technical novelty of our approach is the integration of Multi-level Monte Carlo (MLMC) and Multi-fidelity Monte Carlo (MFMC) that enable data from different time and state representations (system models) to be jointly used to reduce variance and improve sampling efficiency. We also provide theoretical analysis of the proposed method and show that our estimator is unbiased and consistent under mild conditions. Finally, we demonstrate via numerical simulation that the proposed method has improved computation (sampling costs) vs. accuracy trade-offs for risk quantification and path integral control.

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arXiv2026

UAVGENT: A Language-Guided Distributed Control Framework

We study language-in-the-loop control for multi-drone systems that execute evolving, high-level missions while retaining formal robustness guarantees at the physical layer. We propose a three-layer architecture in which (i) a human operator issues natural-language instructions, (ii) an LLM-based supervisor periodically interprets, verifies, and corrects the commanded task in the context of the latest state and target estimates, and (iii) a distributed inner-loop controller tracks the resulting reference using only local relative information. We derive a theoretical guarantee that characterizes tracking performance under bounded disturbances and piecewise-smooth references with discrete jumps induced by LLM updates. Overall, our results illustrate how centralized language-based task reasoning can be combined with distributed feedback control to achieve complex behaviors with provable robustness and stability.

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arXiv2026

Myopically Verifiable Probabilistic Certificates for Safe Control and Learning

This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed 'probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.

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arXiv2026

Polynomial Convergence of Riemannian Diffusion Models

Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data distribution to a noise distribution spanning the whole space, and a backward process, which inverts this transformation to recover the data distribution from noise. Most of the existing literature assumes that the underlying space is Euclidean. However, in many practical applications, the data are constrained to lie on a submanifold of Euclidean space. Addressing this setting, De Bortoli et al. (2022) introduced Riemannian diffusion models and proved that using an exponentially small step size yields a small sampling error in the Wasserstein distance, provided the data distribution is smooth and strictly positive, and the score estimate is $L_\infty$-accurate. In this paper, we greatly strengthen this theory by establishing that, under $L_2$-accurate score estimate, a {\em polynomially small stepsize} suffices to guarantee small sampling error in the total variation distance, without requiring smoothness or positivity of the data distribution. Our analysis only requires mild and standard curvature assumptions on the underlying manifold. The main ingredients in our analysis are Li-Yau estimate for the log-gradient of heat kernel, and Minakshisundaram-Pleijel parametrix expansion of the perturbed heat equation. Our approach opens the door to a sharper analysis of diffusion models on non-Euclidean spaces.

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arXiv2025

Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information

Policy design in non-stationary Markov Decision Processes (MDPs) is inherently challenging due to the complexities introduced by time-varying system transition and reward, which make it difficult for learners to determine the optimal actions for maximizing cumulative future rewards. Fortunately, in many practical applications, such as energy systems, look-ahead predictions are available, including forecasts for renewable energy generation and demand. In this paper, we leverage these look-ahead predictions and propose an algorithm designed to achieve low regret in non-stationary MDPs by incorporating such predictions. Our theoretical analysis demonstrates that, under certain assumptions, the regret decreases exponentially as the look-ahead window expands. When the system prediction is subject to error, the regret does not explode even if the prediction error grows sub-exponentially as a function of the prediction horizon. We validate our approach through simulations, confirming the efficacy of our algorithm in non-stationary environments.

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arXiv2025

Rate-cost tradeoffs in continuous-time control with a biomolecular application

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on the data rate necessary to achieve the desired control cost. The lower bound is attained with equality if the control is performed via an additive white Gaussian channel. The system model approximates the dynamics of a discrete-state molecular birth-death process, and the result has direct implications on the control of a biomolecular system via chemical reactions, where the multiplicative control corresponds to the degradation rate, the additive control corresponds to the production rate, and the control objective is to decrease the fluctuations of the controlled molecular species around their desired concentration levels.

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arXiv2025

Safe Driving in Occluded Environments

Ensuring safe autonomous driving in the presence of occlusions poses a significant challenge in its policy design. While existing model-driven control techniques based on set invariance can handle visible risks, occlusions create latent risks in which safety-critical states are not observable. Data-driven techniques also struggle to handle latent risks because direct mappings from risk-critical objects in sensor inputs to safe actions cannot be learned without visible risk-critical objects. Motivated by these challenges, in this paper, we propose a probabilistic safety certificate for latent risk. Our key technical enabler is the application of probabilistic invariance: It relaxes the strict observability requirements imposed by set-invariance methods that demand the knowledge of risk-critical states. The proposed techniques provide linear action constraints that confine the latent risk probability within tolerance. Such constraints can be integrated into model predictive controllers or embedded in data-driven policies to mitigate latent risks. The proposed method is tested using the CARLA simulator and compared with a few existing techniques. The theoretical and empirical analysis jointly demonstrate that the proposed methods assure long-term safety in real-time control in occluded environments without being overly conservative and with transparency to exposed risks.

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arXiv2025

Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems

Accurate estimation of long-term risk is essential for the design and analysis of stochastic dynamical systems. Existing risk quantification methods typically rely on extensive datasets involving risk events observed over extended time horizons, which can be prohibitively expensive to acquire. Motivated by this gap, we propose an efficient method for learning long-term risk probabilities using short-term samples with limited occurrence of risk events. Specifically, we establish that four distinct classes of long-term risk probabilities are characterized by specific partial differential equations (PDEs). Using this characterization, we introduce a physics-informed learning framework that combines empirical data with physics information to infer risk probabilities. We then analyze the theoretical properties of this framework in terms of generalization and convergence. Through numerical experiments, we demonstrate that our framework not only generalizes effectively beyond the sampled states and time horizons but also offers additional benefits such as improved sample efficiency, rapid online inference capabilities under changing system dynamics, and stable computation of probability gradients. These results highlight how embedding PDE constraints, which contain explicit gradient terms and inform how risk probabilities depend on state, time horizon, and system parameters, improves interpolation and generalization between/beyond the available data.

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arXiv2025

Kalman Bayesian Transformer

Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by balancing new information and previously learned knowledge in the pre-trained models. This challenge is further complicated when training is to be completed in latency-critical environments and learning must additionally quantify and be mediated by uncertainty. Motivated by these challenges, we propose a novel method that frames sequential fine-tuning as a posterior inference problem within a Bayesian framework. Our approach integrates closed-form moment propagation of random variables, Kalman Bayesian Neural Networks, and Taylor approximations of the moments of softmax functions. By explicitly accounting for pre-trained models as priors and adaptively balancing them against new information based on quantified uncertainty, our method achieves robust and data-efficient sequential learning. The effectiveness of our method is demonstrated through numerical simulations involving sequential adaptation of a decision transformer to tasks characterized by distribution shifts and limited memory resources.

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arXiv2025

Neural Spline Operators for Risk Quantification in Stochastic Systems

Accurately quantifying long-term risk probabilities in diverse stochastic systems is essential for safety-critical control. However, existing sampling-based and partial differential equation (PDE)-based methods often struggle to handle complex varying dynamics. Physics-informed neural networks learn surrogate mappings for risk probabilities from varying system parameters of fixed and finite dimensions, yet can not account for functional variations in system dynamics. To address these challenges, we introduce physics-informed neural operator (PINO) methods to risk quantification problems, to learn mappings from varying \textit{functional} system dynamics to corresponding risk probabilities. Specifically, we propose Neural Spline Operators (NeSO), a PINO framework that leverages B-spline representations to improve training efficiency and achieve better initial and boundary condition enforcements, which are crucial for accurate risk quantification. We provide theoretical analysis demonstrating the universal approximation capability of NeSO. We also present two case studies, one with varying functional dynamics and another with high-dimensional multi-agent dynamics, to demonstrate the efficacy of NeSO and its significant online speed-up over existing methods. The proposed framework and the accompanying universal approximation theorem are expected to be beneficial for other control or PDE-related problems beyond risk quantification.

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