In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the optimization procedure, it is necessary to employ a numerical scheme to integrate candidate dynamical systems and assess how their solutions fit the data. This paper reveals potentially serious effects of a chosen numerical scheme on the learning outcome. In particular, our analysis demonstrates that a damped oscillatory system may be incorrectly identified as having "anti-damping" and exhibiting a reversed oscillation direction, despite adequately fitting the given data points.

Photonic device development (PDD) has achieved remarkable success in designing and implementing new devices for controlling light across various wavelengths, scales, and applications, including telecommunications, imaging, sensing, and quantum information processing. PDD is an iterative, five-step process that consists of: i) deriving device behavior from design parameters, ii) simulating device performance, iii) finding the optimal candidate designs from simulations, iv) fabricating the optimal device, and v) measuring device performance. Classically, all these steps involve Bayesian optimization, material science, control theory, and direct physics-driven numerical methods. However, many of these techniques are computationally intractable, monetarily costly, or difficult to implement at scale. In addition, PDD suffers from large optimization landscapes, uncertainties in structural or optical characterization, and difficulties in implementing robust fabrication processes. However, the advent of machine learning over the past decade has provided novel, data-driven strategies for tackling these challenges, including surrogate estimators for speeding up computations, generative modeling for noisy measurement modeling and data augmentation, reinforcement learning for fabrication, and active learning for experimental physical discovery. In this review, we present a comprehensive perspective on these methods to enable machine-learning-assisted PDD (ML-PDD) for efficient design optimization with powerful generative models, fast simulation and characterization modeling under noisy measurements, and reinforcement learning for fabrication. This review will provide researchers from diverse backgrounds with valuable insights into this emerging topic, fostering interdisciplinary efforts to accelerate the development of complex photonic devices and systems.

In was recently established that for convex optimization problems with a sparse optimal solution (may it be entry-wise sparsity or matrix rank-wise sparsity) it is possible to have linear convergence rates which depend on an improved mixed-norm condition number of the form $\frac{β_1{}s}{α_2}$, where $β_1$ is the $\ell_1$-Lipchitz continuity constant of the gradient, $α_2$ is the $\ell_2$-quadratic growth constant, and $s$ is the sparsity of the optimal solution. However, beyond the improved convergence rate, these methods are unable to leverage the sparsity of optimal solutions towards improving also the runtime of each iteration, which may still be prohibitively high for high-dimensional problems. In this work, we establish that linear convergence rates which depend on this improved condition number can be obtained using only sparse updates, which may result in overall significantly improved running times. Moreover, our methods are considerably easier to implement.

--T o gain deeper insights into a complex sensor system through the lens of causality, we present common and individual causal mechanism estimation (CICME), a novel three-step approach to inferring causal mechanisms from heterogeneous data collected across multiple domains. By leveraging the principle of Causal Transfer Learning (CTL), CICME is able to reliably detect domain-invariant causal mechanisms when provided with sufficient samples. The identified common causal mechanisms are further used to guide the estimation of the remaining causal mechanisms in each domain individually. The performance of CICME is evaluated on linear Gaussian models under scenarios inspired from a manufacturing process. Building upon existing continuous optimization-based causal discovery methods, we show that CICME leverages the benefits of applying causal discovery on the pooled data and repeatedly on data from individual domains, and it even outperforms both baseline methods under certain scenarios. In manufacturing systems, sensors are widely deployed to monitor machines, components, and environmental conditions.

Motion control of flexible joint robots (FJR) is challenged by inherent flexibility and configuration-dependent variations in system dynamics. While disturbance observers (DOB) can enhance system robustness, their performance is often limited by the elasticity of the joints and the variations in system parameters, which leads to a conservative design of the DOB. This paper presents a novel frequency response function (FRF)-based optimization method aimed at improving DOB performance, even in the presence of flexibility and system variability. The proposed method maximizes control bandwidth and effectively suppresses vibrations, thus enhancing overall system performance. Closed-loop stability is rigorously proven using the Nyquist stability criterion. Experimental validation on a FJR demonstrates that the proposed approach significantly improves robustness and motion performance, even under conditions of joint flexibility and system variation.

We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a bundle-level (BL) type method that achieves global linear convergence -- to our knowledge, the first such result for any algorithm for this problem class. We extend this method to handle approximately PWS functions and to solve weakly-convex PWS problems, improving the state-of-the-art complexity to match the benchmark for smooth non-convex optimization. Furthermore, we introduce the first verifiable and accurate termination criterion for PWS optimization. Similar to the gradient norm in smooth optimization, this certificate tightly characterizes the optimality gap under the QG condition, and can moreover be evaluated without knowledge of any problem parameters. We develop a search subroutine for this certificate and embed it within a guess-and-check framework, resulting in an almost parameter-free algorithm for both the convex QG and weakly-convex settings.

The increasing adoption of Artificial Intelligence (AI) has led to larger, more complex models with numerous parameters that require substantial computing power -- resources often unavailable in many real-world application scenarios. Our paper addresses this challenge by introducing knowledge grafting, a novel mechanism that optimizes AI models for resource-constrained environments by transferring selected features (the scion) from a large donor model to a smaller rootstock model. The approach achieves an 88.54% reduction in model size (from 64.39 MB to 7.38 MB), while improving generalization capability of the model. Our new rootstock model achieves 89.97% validation accuracy (vs. donor's 87.47%), maintains lower validation loss (0.2976 vs. 0.5068), and performs exceptionally well on unseen test data with 90.45% accuracy. It addresses the typical size vs performance trade-off, and enables deployment of AI frameworks on resource-constrained devices with enhanced performance. We have tested our approach on an agricultural weed detection scenario, however, it can be extended across various edge computing scenarios, potentially accelerating AI adoption in areas with limited hardware/software support -- by mirroring in a similar manner the horticultural grafting enables productive cultivation in challenging agri-based environments.

Resource allocation (RA) is critical to efficient service deployment in Network Function Virtualization (NFV), a transformative networking paradigm. Recently, deep Reinforcement Learning (RL)-based methods have been showing promising potential to address this complexity. However, the lack of a systematic benchmarking framework and thorough analysis hinders the exploration of emerging networks and the development of more robust algorithms while causing inconsistent evaluation. In this paper, we introduce Virne, a comprehensive benchmarking framework for the NFV-RA problem, with a focus on supporting deep RL-based methods. Virne provides customizable simulations for diverse network scenarios, including cloud, edge, and 5G environments. It also features a modular and extensible implementation pipeline that supports over 30 methods of various types, and includes practical evaluation perspectives beyond effectiveness, such as scalability, generalization, and scalability. Furthermore, we conduct in-depth analysis through extensive experiments to provide valuable insights into performance trade-offs for efficient implementation and offer actionable guidance for future research directions. Overall, with its diverse simulations, rich implementations, and extensive evaluation capabilities, Virne could serve as a comprehensive benchmark for advancing NFV-RA methods and deep RL applications. The code is publicly available at https://github.com/GeminiLight/virne.

Fair and dynamic energy allocation in community microgrids remains a critical challenge, particularly when serving socio-economically diverse participants. Static optimization and cost-sharing methods often fail to adapt to evolving inequities, leading to participant dissatisfaction and unsustainable cooperation. This paper proposes a novel framework that integrates multi-objective mixed-integer linear programming (MILP), cooperative game theory, and a dynamic equity-adjustment mechanism driven by reinforcement learning (RL). At its core, the framework utilizes a bi-level optimization model grounded in Equity-regarding Welfare Maximization (EqWM) principles, which incorporate Rawlsian fairness to prioritize the welfare of the least advantaged participants. We introduce a Proximal Policy Optimization (PPO) agent that dynamically adjusts socio-economic weights in the optimization objective based on observed inequities in cost and renewable energy access. This RL-powered feedback loop enables the system to learn and adapt, continuously striving for a more equitable state. To ensure transparency, Explainable AI (XAI) is used to interpret the benefit allocations derived from a weighted Shapley value. Validated across six realistic scenarios, the framework demonstrates peak demand reductions of up to 72.6%, and significant cooperative gains. The adaptive RL mechanism further reduces the Gini coefficient over time, showcasing a pathway to truly sustainable and fair energy communities.

We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian metric induced by a barrier function, we obtain a Riemannian subgradient flow formulated as a differential inclusion, which remains strictly within the interior of the feasible set. This continuous dynamical system unifies two classes of iterative optimization methods, namely the Hessian barrier method and mirror descent scheme, by revealing that these methods can be interpreted as discrete approximations of the continuous flow. We explore the long-term behavior of the trajectories generated by this dynamical system and show that the existing deficient convergence properties of the Hessian barrier and mirror descent scheme can be unifily and more insightfully interpreted through these of the continuous trajectory. For instance, the notorious spurious stationary points \cite{chen2024spurious} observed in Hessian barrier method and mirror descent scheme are interpreted as stable equilibria of the dynamical system that do not correspond to real stationary points of the original optimization problem. We provide two sufficient condition such that these spurious stationary points can be avoided if the strict complementarity conditions holds. In the absence of these regularity condition, we propose a random perturbation strategy that ensures the trajectory converges (subsequentially) to an approximate stationary point. Building on these insights, we introduce two iterative Riemannian subgradient methods, form of interior point methods, that generalizes the existing Hessian barrier method and mirror descent scheme for solving nonsmooth nonconvex optimization problems.