Numerical simulation of complex physical phenomena is a core enabling technology for digital twins, which are comprised of physical and virtual assets with a two-way flow of information: data from the physical asset is used to construct and/or calibrate the virtual asset (a numerical model), while numerical predictions from the virtual asset are used for control or decision-making for the physical asset [42]. To be viable for practical application, the virtual asset must be able to produce predictions rapidly and reliably; however, the underlying physics that are of interest for digital twin applications can typically only be accurately simulated using a large number of degrees of freedom, leading to computationally expensive numerical simulations. The explainability and computational efficiency of decisions made by the digital twin play a key role in safety-critical applications, making explainable artificial intelligence an essential ingredient [24]. Model reduction techniques are one such explainable scientific machine learning technique that construct low-dimensional systems, called reduced-order models (ROMs), to serve as computationally inexpensive surrogates for a high-dimensional physics simulation [4, 20]. This paper introduces a technique for adaptively constructing ROMs to emulate systems with parametric dependence, that is, systems whose behavior varies with some set of parameters, usually representing physical properties. We focus on systems where the parametric dependence manifests in the operators defining the model, not merely in initial conditions or external inputs.

Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d.

The new space might have more or fewer dimensions depending on the goal.

Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and generalization. We introduce a post hoc, model-agnostic framework for predictive uncertainty quantification in latent space ROMs that requires no modification to the underlying architecture or training procedure. Using conformal prediction, our approach estimates statistical prediction intervals for multiple components of the ROM pipeline: latent dynamics, reconstruction, and end-to-end predictions. We demonstrate the method on a latent space dynamical model for cloud microphysics, where it accurately predicts the evolution of droplet-size distributions and quantifies uncertainty across the ROM pipeline.

Claims that humanoid robots achieve ``human-level'' actuation are common but rarely quantified. Peak torque or speed specifications tell us little about whether a joint can deliver the right combination of torque, power, and endurance at task-relevant postures and rates. We introduce a comprehensive framework that makes ``human-level'' measurable and comparable across systems. Our approach has three components. First, a kinematic \emph{DoF atlas} standardizes joint coordinate systems and ranges of motion using ISB-based conventions, ensuring that human and robot joints are compared in the same reference frames. Second, \emph{Human-Equivalence Envelopes (HEE)} define per-joint requirements by measuring whether a robot meets human torque \emph{and} power simultaneously at the same joint angle and rate $(q,ω)$, weighted by positive mechanical work in task-specific bands (walking, stairs, lifting, reaching, and hand actions). Third, the \emph{Human-Level Actuation Score (HLAS)} aggregates six physically grounded factors: workspace coverage (ROM and DoF), HEE coverage, torque-mode bandwidth, efficiency, and thermal sustainability. We provide detailed measurement protocols using dynamometry, electrical power monitoring, and thermal testing that yield every HLAS input from reproducible experiments. A worked example demonstrates HLAS computation for a multi-joint humanoid, showing how the score exposes actuator trade-offs (gearing ratio versus bandwidth and efficiency) that peak-torque specifications obscure. The framework serves as both a design specification for humanoid development and a benchmarking standard for comparing actuation systems, with all components grounded in published human biomechanics data.

Background: Upper-limb weakness and tremor (4--12 Hz) limit activities of daily living (ADL) and reduce adherence to home rehabilitation. Objective: To assess technical feasibility and clinician-relevant signals of a sensor-fused wearable targeting the triceps brachii and extensor pollicis brevis. Methods: A lightweight node integrates surface EMG (1 kHz), IMU (100--200 Hz), and flex/force sensors with on-device INT8 inference (Tiny 1D-CNN/Transformer) and a safety-bounded assist policy (angle/torque/jerk limits; stall/time-out). Healthy adults (n = 12) performed three ADL-like tasks. Primary outcomes: Tremor Index (TI), range of motion (ROM), repetitions (Reps min$^{-1}$). Secondary: EMG median-frequency slope (fatigue trend), closed-loop latency, session completion, and device-related adverse events. Analyses used subject-level paired medians with BCa 95\% CIs; exact Wilcoxon $p$-values are reported in the Results. Results: Assistance was associated with lower tremor prominence and improved task throughput: TI decreased by $-0.092$ (95\% CI [$-0.102$, $-0.079$]), ROM increased by $+12.65\%$ (95\% CI [$+8.43$, $+13.89$]), and Reps rose by $+2.99$ min$^{-1}$ (95\% CI [$+2.61$, $+3.35$]). Median on-device latency was 8.7 ms at a 100 Hz loop rate; all sessions were completed with no device-related adverse events. Conclusions: Multimodal sensing with low-latency, safety-bounded assistance produced improved movement quality (TI $\downarrow$) and throughput (ROM, Reps $\uparrow$) in a pilot technical-feasibility setting, supporting progression to IRB-approved patient studies. Trial registration: Not applicable (pilot non-clinical).

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast approximations. While modern ROMs can solve parameterized families of PDEs, their predictive power degrades over long time horizons. We address this by (1) introducing a flexible, high-order, yet inexpensive finite-difference scheme and (2) proposing a Rollout loss that trains ROMs to make accurate predictions over arbitrary time horizons. We demonstrate our approach on the 2D Burgers equation.

Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g., hybrid zero dynamics. This paper aims to unify these approaches through a layered control perspective. In particular, we establish conditions on when a ROM of locomotion yields stable walking on the full-order hybrid dynamics. To achieve this result, given an ROM we synthesize a zero dynamics manifold encoding the behavior of the ROM -- controllers can be synthesized that drive the FOM to this surface, yielding hybrid zero dynamics. We prove that a stable periodic orbit in the ROM implies an input-to-state stable periodic orbit of the FOM's hybrid zero dynamics, and hence the FOM dynamics. This result is demonstrated in simulation on a linear inverted pendulum ROM and a 5-link planar walking FOM.

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3% error and computational speed-up factor above 19,000.