A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network without imposing any differentiability assumptions. Firstly, a tractable approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints and restricting the right-hand side of the constraints with a proper positive parameter, which will be iteratively solved by a random-fixed projection algorithm. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed feasibility. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and populating the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time convergence of the distributed optimization, a distributed termination algorithm is developed based on uniformly local consensus and zeroth-order optimality under uniformly strongly connected graphs. Fourthly, it is proved that the cutting-surface consensus approach converges within a finite number of iterations. Finally, the effectiveness of the approach is illustrated through a numerical example.

It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and polynomially bounded computational power, under mild assumptions about the distributions of the noise and challenge vectors. This extends the results of Rh\"uramir et al. (2013), who showed a subset of this class of PUFs to be learnable in polynomial time in the absence of noise, under the assumption that the optics of the PUF were either linear or had negligible nonlinear effects. We derive polynomial bounds for the required number of samples and the computational complexity of a linear regression algorithm, based on size parameters of the PUF, the distributions of the challenge and noise vectors, and the probability and accuracy of the regression algorithm, with a similar analysis to one done by Bootle et al. (2018), who demonstrated a learning attack on a poorly implemented version of the Learning With Errors problem.

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic environment. The proposed algorithm is reference-free and utilizes historical data from previous iterations to enhance the performance of the autonomous system. Unlike existing algorithms, the i2LQR computes the optimal solution in an iterative manner at each timestamp, rendering it well-suited for iterative tasks with changing constraints at different iterations. To evaluate the performance of the proposed algorithm, we conduct numerical simulations for an iterative task aimed at minimizing completion time. The results show that i2LQR achieves an optimized performance with respect to learning-based MPC (LMPC) as the benchmark in static environments, and outperforms LMPC in dynamic environments with both static and dynamics obstacles.

We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $O(N)$, which are both optimal. When compiled into the $\{\mathrm{H,S,T,CNOT}\}$ gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error $\epsilon$ in depth $O(\log(N/\epsilon))$ and spacetime allocation $O(N\log(\log(N)/\epsilon))$, improving over $O(\log(N)\log(N/\epsilon))$ and $O(N\log(N/\epsilon))$, respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead -- $O(N)$ ancilla qubits are reused efficiently to prepare a product state of $w$ $N$-dimensional states in depth $O(w + \log(N))$ rather than $O(w\log(N))$, achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket.

For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is exploding, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano- and micro-mechanics, architected materials, and 2D material. Finally, we highlight some current challenges of applying ML to multi-modality and multi-fidelity experimental datasets and propose several future research directions. This review aims to provide valuable insights into the use of ML methods as well as a variety of examples for researchers in solid mechanics to integrate into their experiments.

The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works modeled such data by considering that the node attributes are generated from the node community memberships. In this work, motivated by a recent surge of works in signal processing using deep neural networks as priors, we propose to model the communities as being determined by the node attributes rather than the opposite. We define the corresponding model; we call it the neural-prior SBM. We propose an algorithm, stemming from statistical physics, based on a combination of belief propagation and approximate message passing. We analyze the performance of the algorithm as well as the Bayes-optimal performance. We identify detectability and exact recovery phase transitions, as well as an algorithmically hard region. The proposed model and algorithm can be used as a benchmark for both theory and algorithms. To illustrate this, we compare the optimal performances to the performance of simple graph neural networks.

Explicit antisymmetrization of a neural network is a potential candidate for a universal function approximator for generic antisymmetric functions, which are ubiquitous in quantum physics. However, this procedure is a priori factorially costly to implement, making it impractical for large numbers of particles. The strategy also suffers from a sign problem. Namely, due to near-exact cancellation of positive and negative contributions, the magnitude of the antisymmetrized function may be significantly smaller than before anti-symmetrization. We show that the anti-symmetric projection of a two-layer neural network can be evaluated efficiently, opening the door to using a generic antisymmetric layer as a building block in anti-symmetric neural network Ansatzes. This approximation is effective when the sign problem is controlled, and we show that this property depends crucially the choice of activation function under standard Xavier/He initialization methods. As a consequence, using a smooth activation function requires re-scaling of the neural network weights compared to standard initializations.

One of the essential components of deep learning is the choice of the loss function and performance metrics used to train and evaluate models. This paper reviews the most prevalent loss functions and performance measurements in deep learning. We examine the benefits and limits of each technique and illustrate their application to various deep-learning problems. Our review aims to give a comprehensive picture of the different loss functions and performance indicators used in the most common deep learning tasks and help practitioners choose the best method for their specific task.

While existing literature encompasses exoskeleton-assisted sit-stand tasks, the integration of energy recovery mechanisms remains unexplored. To push these boundaries further, this study introduces a portable pneumatic knee exoskeleton that operates in both quasi-passive and active modes, where active mode is utilized for aiding in standing up (power generation), thus the energy flows from the exoskeleton to the user, and quasi-passive mode for aiding in sitting down (power absorption), where the device absorbs and can store energy in the form of compressed air, leading to energy savings in active mode. The absorbed energy can be stored and later reused without compromising exoskeleton transparency in the meantime. In active mode, a small air pump inflates the pneumatic artificial muscle (PAM), which stores the compressed air, that can then be released into a pneumatic cylinder to generate torque. All electronic and pneumatic components are integrated into the system, and the exoskeleton weighs 3.9 kg with a maximum torque of 20 Nm at the knee joint. The paper describes the mechatronic design, mathematical model and includes a pilot study with an able-bodied subject performing sit-to-stand tasks. The results show that the exoskeleton can recover energy while assisting the subject and reducing muscle activity. Furthermore, results underscore air regeneration's impact on energy-saving in portable pneumatic exoskeletons.