Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the model coefficients by removing library elements from consideration. By introducing an annealing scheme that reactivates a fraction of the removed terms with a cooling schedule, we are able to improve the performance of these sparse learning algorithms. We concentrate on two approaches to the optimization, SINDy, and an alternative using hard thresholding pursuit. We see in both cases that annealing can improve model accuracy. The effectiveness of annealing is demonstrated through comparisons on several nonlinear systems pulled from convective flows, excitable systems, and population dynamics. Finally we apply these algorithms to experimental data for projectile motion.

High-dimensional partial differential equations (PDEs) pose significant computational challenges across fields ranging from quantum chemistry to economics and finance. Although scientific machine learning (SciML) techniques offer approximate solutions, they often suffer from bias and neglect crucial physical insights. Inspired by inference-time scaling strategies in language models, we propose Simulation-Calibrated Scientific Machine Learning (SCaSML), a physics-informed framework that dynamically refines and debiases the SCiML predictions during inference by enforcing the physical laws. SCaSML leverages derived new physical laws that quantifies systematic errors and employs Monte Carlo solvers based on the Feynman-Kac and Elworthy-Bismut-Li formulas to dynamically correct the prediction. Both numerical and theoretical analysis confirms enhanced convergence rates via compute-optimal inference methods. Our numerical experiments demonstrate that SCaSML reduces errors by 20-50% compared to the base surrogate model, establishing it as the first algorithm to refine approximated solutions to high-dimensional PDE during inference. Code of SCaSML is available at https://github.com/Francis-Fan-create/SCaSML.

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage. Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.

Generating natural and physically plausible character motion remains challenging, particularly for long-horizon control with diverse guidance signals. While prior work combines high-level diffusion-based motion planners with low-level physics controllers, these systems suffer from domain gaps that degrade motion quality and require task-specific fine-tuning. To tackle this problem, we introduce UniPhys, a diffusion-based behavior cloning framework that unifies motion planning and control into a single model. UniPhys enables flexible, expressive character motion conditioned on multi-modal inputs such as text, trajectories, and goals. To address accumulated prediction errors over long sequences, UniPhys is trained with the Diffusion Forcing paradigm, learning to denoise noisy motion histories and handle discrepancies introduced by the physics simulator. This design allows UniPhys to robustly generate physically plausible, long-horizon motions. Through guided sampling, UniPhys generalizes to a wide range of control signals, including unseen ones, without requiring task-specific fine-tuning. Experiments show that UniPhys outperforms prior methods in motion naturalness, generalization, and robustness across diverse control tasks.

In this paper, we propose a collaborative shelf-picking framework that combines multimodal interaction, physics-based reasoning, and task division for enhanced human-robot teamwork. The framework enables the robot to recognize human pointing gestures, interpret verbal cues and voice commands, and communicate through visual and auditory feedback. Moreover, it is powered by a Large Language Model (LLM) which utilizes Chain of Thought (CoT) and a physics-based simulation engine for safely retrieving cluttered stacks of boxes on shelves, relationship graph for sub-task generation, extraction sequence planning and decision making.

Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the field. We also discuss PDE-specific operator learning, outlining strategies for incorporating physical and mathematical constraints into architecture design and training processes. Finally, we end by highlighting key future directions such as active data collection and the development of rigorous uncertainty quantification frameworks.

S automation advances, robots are increasingly utilized for complex tasks, reducing manual labor in hazardous environments while improving efficiency, precision, and cost-effectiveness [1]. However, real-world robotic applications require seamless interaction with deformable objects, which presents significant challenges due to material flexibility and unpredictable shape changes [2]. Unlike rigid object manipulation, deformable object manipulation (DOM) requires real-time adaptive control to compensate for continuous state variations and external forces. Traditional physics-based control models, such as mass-spring systems and finite element methods [3], [4], [5], attempt to model deformable object behavior but often fall short in real-world applications due to the sensitvity of control parameters and the difficulty of modeling complex contact dynamics. To address these limitations, recent research has shifted toward machine learning and data-driven approaches, where robots learn from sensor feedback or demonstrations rather than relying on hard-coded models [6]. Predictive learning models [7], [8], [9] have proven effective for latent space learning and object behavior forecasting, improving adaptability across applications such as fabric repositioning [10], crop harvesting [11], [12], medical robotics [13], and deformable linear object manipulation [14], [15]. While significant progress has been made in DOM, little research has focused on deformable tool manipulation (DTM), which introduces additional complexities such as bending dynamics, force regulation, and stability issues.

This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.

We present a versatile latent representation that enables physically simulated character to efficiently utilize motion priors. To build a powerful motion embedding that is shared across multiple tasks, the physics controller should employ rich latent space that is easily explored and capable of generating high-quality motion. We propose integrating continuous and discrete latent representations to build a versatile motion prior that can be adapted to a wide range of challenging control tasks. Specifically, we build a discrete latent model to capture distinctive posterior distribution without collapse, and simultaneously augment the sampled vector with the continuous residuals to generate high-quality, smooth motion without jittering. We further incorporate Residual Vector Quantization, which not only maximizes the capacity of the discrete motion prior, but also efficiently abstracts the action space during the task learning phase. We demonstrate that our agent can produce diverse yet smooth motions simply by traversing the learned motion prior through unconditional motion generation. Furthermore, our model robustly satisfies sparse goal conditions with highly expressive natural motions, including head-mounted device tracking and motion in-betweening at irregular intervals, which could not be achieved with existing latent representations.

Causal reasoning and compositional reasoning are two core aspirations in generative AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously, termed compositional causal reasoning (CCR): the ability to infer how causal measures compose and, equivalently, how causal quantities propagate through graphs. We instantiate a framework for the systematic evaluation of CCR for the average treatment effect and the probability of necessity and sufficiency. As proof of concept, we demonstrate the design of CCR tasks for language models in the LLama, Phi, and GPT families. On a math word problem, our framework revealed a range of taxonomically distinct error patterns. Additionally, CCR errors increased with the complexity of causal paths for all models except o1.