Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary control of coupled PDEs, coupled Goursat-form PDEs govern two or more gain kernels -- a PDE structure unaddressed thus far with DeepONet. In this note, we open the subject of approximating systems of gain kernel PDEs for hyperbolic PDE plants by considering a simple counter-convecting $2\times 2$ coupled system in whose control a $2\times 2$ kernel PDE systems in Goursat form arises. Applications include oil drilling, Saint-Venant model of shallow water waves, and Aw-Rascle-Zhang model of stop-and-go instability in congested traffic flow. In this paper we establish the continuity of the mapping from (a total of five) plant PDE functional coefficients to the kernel PDE solutions, prove the existence of an arbitrarily close DeepONet approximation to the kernel PDEs, and establish that the DeepONet-approximated gains guarantee stabilization when replacing the exact backstepping gain kernels. Taking into account anti-collocated boundary actuation and sensing, our $L^2$\emph{-Globally-exponentially} stabilizing (GES) approximate gain kernel-based output feedback design implies the deep learning of both the controller's and the observer's gains. Moreover, the encoding of the output-feedback law into DeepONet ensures \emph{semi-global practical exponential stability (SG-PES).} The DeepONet operator speeds up the computation of the controller gains by multiple orders of magnitude. Its theoretically proven stabilizing capability is demonstrated through simulations.

We investigate the applicability of machine learning technologies to the development of parsimonious, interpretable, catchment-scale hydrologic models using directed-graph architectures based on the mass-conserving perceptron (MCP) as the fundamental computational unit. Here, we focus on architectural complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments. The goal is to discover a minimal representation (numbers of cell-states and flow paths) that represents the dominant processes that can explain the input-state-output behaviors of a given catchment, with particular emphasis given to simulating the full range (high, medium, and low) of flow dynamics. We find that a HyMod-like architecture with three cell-states and two major flow pathways achieves such a representation at our study location, but that the additional incorporation of an input-bypass mechanism significantly improves the timing and shape of the hydrograph, while the inclusion of bi-directional groundwater mass exchanges significantly enhances the simulation of baseflow. Overall, our results demonstrate the importance of using multiple diagnostic metrics for model evaluation, while highlighting the need for designing training metrics that are better suited to extracting information across the full range of flow dynamics. Further, they set the stage for interpretable regional-scale MCP-based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes.

Flow image super-resolution (FISR) aims at recovering high-resolution turbulent velocity fields from low-resolution flow images. Existing FISR methods mainly process the flow images in natural image patterns, while the critical and distinct flow visual properties are rarely considered. This negligence would cause the significant domain gap between flow and natural images to severely hamper the accurate perception of flow turbulence, thereby undermining super-resolution performance. To tackle this dilemma, we comprehensively consider the flow visual properties, including the unique flow imaging principle and morphological information, and propose the first flow visual property-informed FISR algorithm. Particularly, different from natural images that are constructed by independent RGB channels in the light field, flow images build on the orthogonal UVW velocities in the flow field. To empower the FISR network with an awareness of the flow imaging principle, we propose quaternion spatial modeling to model this orthogonal spatial relationship for improved FISR. Moreover, due to viscosity and surface tension characteristics, fluids often exhibit a droplet-like morphology in flow images. Inspired by this morphological property, we design the dynamic flow convolution to effectively mine the morphological information to enhance FISR. Extensive experiments on the newly acquired flow image datasets demonstrate the state-of-the-art performance of our method. Code and data will be made available.

Optimization of expensive, noisy, black-box functions commonly occurs in designing sustainable process systems; we review some motivating applications in Section 2 below. In principle, one can apply any type of derivativefree optimization (DFO) method [2] to tackle such problems; however, these methods may require a large number of evaluations to converge. When evaluations of f are expensive, we desire an intelligent sample selection strategy that accounts for all available information to select future samples. The BO framework provides a systematic and versatile way to identify highly informative design candidates using minimal function evaluations. This article reviews recent advances in BO methods and highlights their relevance to design of next-generation sustainable energy and process systems. We also offer some perspectives on future research directions and associated challenges.

This paper presents a modeling effort to explore the underlying physics of temperature evolution during additive friction stir deposition (AFSD) by a human-AI teaming approach. AFSD is an emerging solid-state additive manufacturing technology that deposits materials without melting. However, both process modeling and modeling of the AFSD tool are at an early stage. In this paper, a human-AI teaming approach is proposed to combine models based on first principles with AI. The resulting human-informed machine learning method, denoted as AFSD-Physics, can effectively learn the governing equations of temperature evolution at the tool and the build from in-process measurements. Experiments are designed and conducted to collect in-process measurements for the deposition of aluminum 7075 with a total of 30 layers. The acquired governing equations are physically interpretable models with low computational cost and high accuracy. Model predictions show good agreement with the measurements. Experimental validation with new process parameters demonstrates the model's generalizability and potential for use in tool temperature control and process optimization.

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets) stand out as the leading techniques for solving partial differential equations by incorporating both physical equations and experimental data. However, training PINNs and DeepONets requires significant computational resources, including long computational times and large amounts of memory. In search of computational efficiency, training neural networks using half precision (float16) rather than the conventional single (float32) or double (float64) precision has gained substantial interest, given the inherent benefits of reduced computational time and memory consumed. However, we find that float16 cannot be applied to SciML methods, because of gradient divergence at the start of training, weight updates going to zero, and the inability to converge to a local minima. To overcome these limitations, we explore mixed precision, which is an approach that combines the float16 and float32 numerical formats to reduce memory usage and increase computational speed. Our experiments showcase that mixed precision training not only substantially decreases training times and memory demands but also maintains model accuracy. We also reinforce our empirical observations with a theoretical analysis. The research has broad implications for SciML in various computational applications.

Extracting consistent statistics between relevant free-energy minima of a molecular system is essential for physics, chemistry and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we develop an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one Normalizing Flow (NF) and one MLP per state. We simulate several Markov chains in parallel until they reach convergence, sampling the Boltzmann distribution with an efficient use of energy evaluations. At each iteration, we compute the energy of a subset of the NF-generated configurations using Density Functional Theory (DFT), we predict the remaining configuration's energy with the MLP and actively train the MLP using the DFT-computed energies. Leveraging the trained NF and MLP models, we can compute thermodynamic observables such as free-energy differences or optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster, belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

We propose a scheme leveraging reinforcement learning to engineer control fields for generating non-classical states. It is exemplified by the application to prepare spin squeezed state for an open collective spin model where a linear control term is designed to govern the dynamics. The reinforcement learning agent determines the temporal sequence of control pulses, commencing from coherent spin state in an environment characterized by dissipation and dephasing. When compared to constant control scenarios, this approach provides various control sequences maintaining collective spin squeezing and entanglement. It is observed that denser application of the control pulses enhances the performance of the outcomes. Furthermore, there is a minor enhancement in the performance by adding control actions. The proposed strategy demonstrates increased effectiveness for larger systems. And thermal excitations of the reservoir are detrimental to the control outcomes. It should be confirmed that this is an open-loop strategy by closed-loop simulation, circumventing collapse of quantum state induced by measurements. Thanks to the flexible replaceability of the optimization modules and the controlled system, this research paves the way for its application in manipulating other quantum systems.

Machine learning techniques are now integral to the advancement of intelligent urban services, playing a crucial role in elevating the efficiency, sustainability, and livability of urban environments. The recent emergence of foundation models such as ChatGPT marks a revolutionary shift in the fields of machine learning and artificial intelligence. Their unparalleled capabilities in contextual understanding, problem solving, and adaptability across a wide range of tasks suggest that integrating these models into urban domains could have a transformative impact on the development of smart cities. Despite growing interest in Urban Foundation Models~(UFMs), this burgeoning field faces challenges such as a lack of clear definitions, systematic reviews, and universalizable solutions. To this end, this paper first introduces the concept of UFM and discusses the unique challenges involved in building them. We then propose a data-centric taxonomy that categorizes current UFM-related works, based on urban data modalities and types. Furthermore, to foster advancement in this field, we present a promising framework aimed at the prospective realization of UFMs, designed to overcome the identified challenges. Additionally, we explore the application landscape of UFMs, detailing their potential impact in various urban contexts. Relevant papers and open-source resources have been collated and are continuously updated at https://github.com/usail-hkust/Awesome-Urban-Foundation-Models.

While generative AI is now widespread and useful in society, there are potential risks of misuse, e.g., unconsciously influencing cognitive processes or decision-making. Although this causes a security problem in the cognitive domain, there has been no research about neural and computational mechanisms counteracting the impact of malicious generative AI in humans. We propose DecNefGAN, a novel framework that combines a generative adversarial system and a neural reinforcement model. More specifically, DecNefGAN bridges human and generative AI in a closed-loop system, with the AI creating stimuli that induce specific mental states, thus exerting external control over neural activity. The objective of the human is the opposite, to compete and reach an orthogonal mental state. This framework can contribute to elucidating how the human brain responds to and counteracts the potential influence of generative AI.