Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

BACON allows computational resources to be focused on simulations that provide the most value in terms of reducing epistemic uncertainty.

We present an approach for lifelong/continual learning of convolutional neural networks (CNN) that does not suffer from the problem of catastrophic forgetting when moving from onetask totheother. Weshowthat theactivation maps generated by the CNN trained on the old task can be calibrated using very few calibration parameters, to become relevant to the new task.

We present an approach for lifelong/continual learning of convolutional neural networks (CNN) that does not suffer from the problem of catastrophic forgetting when moving from one task to the other. We show that the activation maps generated by the CNN trained on the old task can be calibrated using very few calibration parameters, to become relevant to the new task. Based on this, we calibrate the activation maps produced by each network layer using spatial and channel-wise calibration modules and train only these calibration parameters for each new task in order to perform lifelong learning. Our calibration modules introduce significantly less computation and parameters as compared to the approaches that dynamically expand the network. Our approach is immune to catastrophic forgetting since we store the task-adaptive calibration parameters, which contain all the task-specific knowledge and is exclusive to each task. Further, our approach does not require storing data samples from the old tasks, which is done by many replay based methods. We perform extensive experiments on multiple benchmark datasets (SVHN, CIFAR, ImageNet, and MS-Celeb), all of which show substantial improvements over state-of-the-art methods (e.g., a 29% absolute increase in accuracy on CIFAR-100 with 10 classes at a time).

UTONOMOUS vehicles are poised to revolutionize transportation by improving road safety, reducing traffic congestion, and increasing mobility convenience [1]. To perceive and interact with their environment accurately, these vehicles rely on a combination of complementary sensors, including LiDAR, RADAR, and cameras. Each sensor offers unique advantages: cameras capture rich visual detail, LiDAR provides precise 3D spatial measurements, and RADAR performs robustly under adverse weather conditions [2]. Sensor fusion leverages the strengths of these modalities to ensure redundancy and resilience, allowing the vehicle to maintain accurate perception in diverse and dynamic environments [3]. A critical component of sensor fusion is extrinsic calibration, which involves the determination of the relative positions and orientations of sensors in a common coordinate frame. However, maintaining precise calibration over time is a persistent challenge. Factors such as mechanical vibrations, temperature changes, and minor collisions can lead to sensor drift, where even small misalignments in sensor orientation or position can result in substantial perception errors, potentially compromising vehicle safety.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector δ, guiding generation toward more reliable reasoning. Experiments on MA TH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4 fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and δ in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. Test-time scaling (TTS) is a practical alternative to ever-larger training, enabling models to "think longer" at inference by allocating additional computation to reasoning. As these studies suggest, TTS allows smaller LLMs to match or even outperform larger ones, providing a more cost-efficient and flexible inference strategy. Despite these benefits, simply increasing test-time compute does not guarantee optimal performance. Recent work has shown that inference without effective verification is often sub-optimal, as models may spend additional computation on low-quality reasoning paths (Setlur et al., 2025). To overcome this inefficiency, we propose a general test-time calibration framework that strategically reallocates the inference budget by leveraging feedback from a verifier or reward model during inference. Rather than treating generation as a fixed forward pass, the model adaptively steers toward high-reward (likely correct) regions, improving reasoning reliability under a fixed query budget. The reward is defined as the inverse distance to the target plus noise.

Visual-inertial fusion is crucial for a large amount of intelligent and autonomous applications, such as robot navigation and augmented reality. To bootstrap and achieve optimal state estimation, the spatial-temporal displacements between IMU and cameras must be calibrated in advance. Most existing calibration methods adopt continuous-time state representation, more specifically the B-spline. Despite these methods achieve precise spatial-temporal calibration, they suffer from high computational cost caused by continuous-time state representation. To this end, we propose a novel and extremely efficient calibration method that unleashes the power of discrete-time state representation. Moreover, the weakness of discrete-time state representation in temporal calibration is tackled in this paper. With the increasing production of drones, cellphones and other visual-inertial platforms, if one million devices need calibration around the world, saving one minute for the calibration of each device means saving 2083 work days in total. To benefit both the research and industry communities, our code will be open-source.

This thesis introduces "Embodied Spatial Intelligence" to address the challenge of creating robots that can perceive and act in the real world based on natural language instructions. To bridge the gap between Large Language Models (LLMs) and physical embodiment, we present contributions on two fronts: scene representation and spatial reasoning. For perception, we develop robust, scalable, and accurate scene representations using implicit neural models, with contributions in self-supervised camera calibration, high-fidelity depth field generation, and large-scale reconstruction. For spatial reasoning, we enhance the spatial capabilities of LLMs by introducing a novel navigation benchmark, a method for grounding language in 3D, and a state-feedback mechanism to improve long-horizon decision-making. This work lays a foundation for robots that can robustly perceive their surroundings and intelligently act upon complex, language-based commands.

We present an approach for lifelong/continual learning of convolutional neural networks (CNN) that does not suffer from the problem of catastrophic forgetting when moving from one task to the other. We show that the activation maps generated by the CNN trained on the old task can be calibrated using very few calibration parameters, to become relevant to the new task.