Input-output Mapping Research Articles

New insights into binocular rivalry from the reconstruction of evolving percepts using model network dynamics.

When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, we derive a linear input-output mapping rooted in the non-linear network dynamics and iteratively apply compressive sensing techniques for signal recovery. Utilizing a dominance metric, we are able to identify when percept alternations occur and use data collected during each dominance period to generate a sequence of percept reconstructions. We show that despite the approximate nature of the input-output mapping and the significant reduction in neurons downstream relative to stimulus pixels, the dominant monocular image is well-encoded in the network dynamics and improvements are garnered when realistic spatial receptive field structure is incorporated into the feedforward connectivity. Our model demonstrates gamma-distributed dominance durations and well obeys Levelt's four laws for how dominance durations change with stimulus strength, agreeing with key recurring experimental observations often used to benchmark rivalry models. In light of evidence that individuals with autism exhibit relatively slow percept switching in binocular rivalry, we corroborate the ubiquitous hypothesis that autism manifests from reduced inhibition in the brain by systematically probing our model alternation rate across choices of inhibition strength. We exhibit sufficient conditions for producing binocular rivalry in the context of natural scene stimuli, opening a clearer window into the dynamic brain computations that vary with the generated percept and a potential path toward further understanding neurological disorders.

A method for real-time mechanical characterisation of microcapsules

Characterising the mechanical properties of flowing microcapsules is important from both fundamental and applied points of view. In the present study, we develop a novel multilayer perceptron (MLP)-based machine learning (ML) approach, for real-time simultaneous predictions of the membrane mechanical law type, shear and area-dilatation moduli of microcapsules, from their camera-recorded steady profiles in tube flow. By MLP, we mean a neural network where many perceptrons are organised into layers. A perceptron is a basic element that conducts input–output mapping operation. We test the performance of the present approach using both simulation and experimental data. We find that with a reasonably high prediction accuracy, our method can reach an unprecedented low prediction latency of less than 1 millisecond on a personal computer. That is the overall computational time, without using parallel computing, from a single experimental image to multiple capsule mechanical parameters. It is faster than a recently proposed convolutional neural network-based approach by two orders of magnitude, for it only deals with the one-dimensional capsule boundary instead of the entire two-dimensional capsule image. Our new approach may serve as the foundation of a promising tool for real-time mechanical characterisation and online active sorting of deformable microcapsules and biological cells in microfluidic devices.

Scalable Nanophotonic-Electronic Spiking Neural Networks

Spiking neural networks (SNN) provide a new computational paradigm capable of highly parallelized, real-time processing. Photonic devices are ideal for the design of high-bandwidth, parallel architectures matching the SNN computational paradigm. Furthermore, the co-integration of CMOS and photonic elements combineslow-loss photonic devices with analog electronics for greater flexibility of nonlinear computational elements. We designed and simulated an optoelectronic spiking neuron circuit on a monolithic silicon photonics (SiPh) process that replicates useful spiking behaviors beyond the leaky integrate-and-fire (LIF). Additionally, we explored two learning algorithms with the potential for on-chip learning using Mach-Zehnder Interferometric (MZI) meshes as synaptic interconnects. A variation of Random Backpropagation (RPB) was experimentally demonstrated on-chip and matched the performance of a standard linear regression on a simple classification task. In addition, we applied the Contrastive Hebbian Learning (CHL) rule to a simulated neural network composed of MZI meshes for a random input-output mapping task. The CHL-trained MZI network performed better than random guessing but did not match the performance of the ideal neural network (without the constraints imposed by the MZI meshes). Through these efforts, we demonstrate that co-integrated CMOS and SiPh technologies are well-suited to the design of scalable SNN computing architectures.

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. We demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

Collateralizing ventral subiculum melanocortin 4 receptor circuits regulate energy balance and food motivation

Hippocampal dysfunction is associated with major depressive disorder, a serious mental illness characterized by not only depressed mood but also appetite disturbance and dysregulated body weight. However, the underlying mechanisms by which hippocampal circuits regulate metabolic homeostasis remain incompletely understood. Here we show that collateralizing melanocortin 4 receptor (MC4R) circuits in the ventral subiculum (vSUB), one of the major output structures of the hippocampal formation, affect food motivation and energy balance. Viral-mediated cell type- and projection-specific input-output circuit mapping revealed that the nucleus accumbens shell (NAcSh)-projecting vSUBMC4R+ neurons send extensive collateral projections of to various hypothalamic nuclei known to be important for energy balance, including the arcuate, ventromedial and dorsomedial nuclei, and receive monosynaptic inputs mainly from the ventral CA1 and the anterior paraventricular nucleus of thalamus. Chemogenetic activation of NAcSh-projecting vSUBMC4R+neurons lead to increase in motivation to obtain palatable food without noticeable effect on homeostatic feeding. Viral-mediated restoration of MC4R signaling in the vSUB partially restores obesity in MC4R-null mice without affecting anxiety- and depression-like behaviors. Collectively, these results delineate vSUBMC4R+ circuits to the unprecedented level of precision and identify the vSUBMC4R signaling as a novel regulator of food reward and energy balance.

Saturating PI Control of Stable Nonlinear Systems Using Singular Perturbations

This article presents an antiwindup propor- tional-integral (PI) controller, using a saturating integrator, for a single-input and single-output (SISO) stable nonlinear plant, whose steady-state input–output map is increasing. We prove that, under reasonable assumptions, there exists an upper bound on the controller gain such that for any constant reference input, the corresponding equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. When the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. The closed-loop stability analysis employs Lyapunov methods in the framework of the singular perturbations theory. Finally, we show that if the plant satisfies the asymptotic gain property, then the closed-loop system is globally asymptotically stable for any sufficiently small controller gain. The effectiveness of the proposed PI controller is proved by showing how it performs as part of the control algorithm of a synchronverter (a special type of dc to ac power converter).

The roles of Kerr nonlinearity in a bosonic quantum neural network

The emerging technology of quantum neural networks (QNNs) offers a quantum advantage over classical artificial neural networks (ANNs) in terms of speed or efficiency of information processing tasks. It is well established that nonlinear mapping between input and output is an indispensable feature of classical ANNs, while in a QNN the roles of nonlinearity are not yet fully understood. As one tends to think of QNNs as physical systems, it is natural to think of nonlinear mapping originating from a physical nonlinearity of the system, such as Kerr nonlinearity. Here we investigate the effect of Kerr nonlinearity on a bosonic QNN in the context of both classical (simulating an XOR gate) and quantum (generating Schrödinger cat states) tasks. Aside offering a mechanism of nonlinear input-output mapping, Kerr nonlinearity reduces the effect of noise or losses, which are particularly important to consider in the quantum setting. We note that nonlinear mapping may also be introduced through a nonlinear input-output encoding rather than a physical nonlinearity: for example, an output intensity is already a nonlinear function of input amplitude. While in such cases Kerr nonlinearity is not strictly necessary, it still increases the performance in the face of noise or losses.

Integrated data-driven modeling and experimental optimization of granular hydrogel matrices

Integrated data-driven modeling and experimental optimization of granular hydrogel matrices

Simple deep-learning approach for α -decay half-life studies

To exploit the potential of deep learning (DL) in $\ensuremath{\alpha}$-decay studies, we refocus on the essence of DL, which is a nonlinear input-output mapping with a hierarchical learning process. Here, instead of using the residual between experimental data and the calculation, the idea of training DL directly by experimental $\ensuremath{\alpha}$-decay half-life is used. The Levenberg-Marquardt backpropagation algorithm is utilized for fixing free parameters of the mapping. A $\mathcal{K}$-fold cross-validation method is introduced to avoid overfitting and improve the generalization performance of DL, as well as to determine hyperparameters effectively. We find that DL results with both three-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and four-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}},l}$ input vectors achieve an impressive accuracy that matches or even exceeds the traditional models. Especially, DL realizes an efficient extraction of the pertinent shell and odd-even staggering effects of half-life solely from the characteristics of ${Q}_{\ensuremath{\alpha}}$ values. On the other hand, the universal decay law (UDL) describes the classical relationship between ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and a-decay half-life, which is homologous with DL. Heuristically, we add the contributions of the angular momentum and blocking effect of unpaired nucleons in the UDL and develop an improved UDL formula.

A novel implementation of an uncertain dead-zone-input-equipped extended state observer and sign estimator

This paper presents a novel implementation based on the observer and estimator for a class of nonlinear systems subject to remarkable control gain variation in the presence of the dead-zone actuator. Specifically, an approximation function of the dead-zone nonlinearity is developed to overcome the non-differentiable problem so that an extended state observer (ESO) can estimate the uncertain dead-zone input. Then, a sign-projected gradient-based estimator is applied to identify the control gain and disturbances for separate compensation. In addition, the output error is decoupled from the estimation error, and the finite-gain stability with exponential and ultimate boundedness is obtained through a defined input–output mapping. Finally, comprehensive comparisons with existing methods on a brushless DC motor illustrate the strong performance and robustness of the proposed design.

A CNN-Based Sentinel-2 Image Super-Resolution Method Using Multiobjective Training

Deep learning methods have become ubiquitous tools in many Earth observation applications, delivering state-of-the-art results while proving to generalize for a variety of scenarios. One such domain concerns the Sentinel-2 (S2) satellite mission, which provides multispectral images in the form of 13 spectral bands, captured at three different spatial resolutions: 10, 20, and 60 m. This research aims to provide a super-resolution mechanism based on fully convolutional neural networks (CNNs) for upsampling the low-resolution (LR) spectral bands of S2 up to 10-m spatial resolution. Our approach is centered on attaining good performance with respect to two main properties: consistency and synthesis. While the synthesis evaluation, also known as Wald’s protocol, has spoken for the performance of almost all previously introduced methods, the consistency property has been overlooked as a viable evaluation procedure. Recently introduced techniques make use of sensor’s modulation transfer function (MTF) to learn an approximate inverse mapping from LR to high-resolution images, which is on a direct path for achieving a good consistency value. To this end, we propose a multiobjective loss for training our architectures, including an MTF-based mechanism, a direct input–output mapping using synthetically degraded data, along with direct similarity measures between high-frequency details from already available 10-m bands, and super-resolved images. Experiments indicate that our method is able to achieve a good tradeoff between consistency and synthesis properties, along with competitive visual quality results.

Extremum seeking for infinite-dimensional systems

The last year was the centennial of the 1922 invention, in the context of maximizing the power transfer to an electric tram car, of the method for real-time model-free optimization called extremum seeking (ES). Forgotten after a few decades of practical use and attempts at theoretical study, ES returned to life when the stability of its operation for not only static input–output maps but for dynamic systems modeled by general nonlinear ordinary differential equations (ODEs) was proven in 1997. Then it is natural to ask “why limit the use and the theoretical advances of ES to ODE systems?” So many—if not the majority of physical systems—involve delays or are modeled by partial differential equations (PDEs); why not pursue the application of ES in the presence of delays and for PDE systems? With this tutorial paper, we show a small portion of the vast space of possibilities of designing ES algorithms for infinite-dimensional systems governed by transport hyperbolic PDEs as well as diffusion parabolic PDEs.

Immersion of nonlinear systems comprising holonomic functions

This paper proposes a model simplification method for nonlinear systems comprising holonomic functions. A holonomic function is a nonlinear function that can be associated with a set of partial differential equations called a Pfaffian system, which contains only rational functions in the variable. By considering the Pfaffian system satisfied by all the holonomic functions in the original nonlinear system, it can be extended to another nonlinear system comprising only rational functions in a new state. This conversion of nonlinear systems can be shown to be an immersion, which preserves the input-output map of the original nonlinear system.

Vision-Based Nonlinear Incremental Control for a Morphing Wing With Mechanical Imperfections

Morphing structures have acquired much attention in the aerospace community because they enable an aircraft to actively adapt its shape during flight, leading to fewer emissions and fuel consumption. Researchers have designed, manufactured, and tested a morphing wing named SmartX-Alpha, which can actively alleviate loads while achieving the optimal lift distribution. However, the widely existing mechanical imperfections can degrade the performance of the morphing wing and even lead to instabilities. To tackle these issues, this article proposes a vision-based adaptive control approach to actively compensate for mechanical imperfections. In this approach, an incremental model is constructed online to identify the system dynamics using servo commands and vision measurements, and then, nonlinear dynamic inversion control is applied based on the identified model. This data-driven control approach with visual feedback has been validated by real-world experiments on the SmartX-Alpha. The results demonstrate that the vision-based system combined with the proposed control methodology can actively compensate for mechanical imperfections with minimal adjustments to the actual system design. Compared to a controller that only uses a feedforward input-output mapping, this proposed approach improves the system performance and decreases the tracking errors by more than 62% despite disturbances. The results collectively demonstrate the effectiveness of the proposed control system, which sets a foundation for realizing morphing in next-generation aircraft.

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive training procedure of a neural network that directly approximates an input-output map of the underlying PDE-constrained optimization problem. The training process thereby focuses on the construction of an accurate surrogate model solely related to the optimization path of an outer iterative optimization loop. True evaluations of the objective function are used to finally obtain certified results. Numerical experiments are given to evaluate the accuracy and efficiency of the approach for a heterogeneous five-spot benchmark problem.

Metaverse Simulation Based on VR, Blockchain, and Reinforcement Learning Model

Abstract: With advancements in virtual reality and the boom of the Metaverse, the technology underlying modern games is progressing rapidly. Virtual reality and current Artificial Intelligence algorithms have resulted in impressive results and immersive user experiences. This proposed work aims to create a first-person blockchain figure VR environment incorporating reinforcement learning and imitation learning methods. Supervised and reinforcement learning work using input-output mapping, but the critical difference is that reinforcement learning uses reward and penalty, which are positive and negative action indicators, respectively. The blockchain-based non-fungible agent, based on this indication, learns which actions are favourable. For a better experience, these profitable actions with imitation learning in the state action format are mapped further. In this environment, reinforcement learning is trained with various parameters such as Sensory complexity, Logic complexity for solving tasks, social complexity, and Physical complexity. This simulation enables users to use NFT guns to shoot enemy agents. These agents have been trained to navigate the map using Reinforcement and Imitation learning and shoot us whenever they sense our presence. The simulation is complete if the user kills every agent before his health level finishes. This proposed work highlights the potential of VR, Blockchain, and reinforcement learning in making Metaverse more interactive and impressive

Reactive power control in photovoltaic systems through (explainable) artificial intelligence

Across the world, efforts to support the energy transition and halt climate change have resulted in significant growth of the number of renewable distributed generators (DGs) installed over the last decade, among which photovoltaic (PV) systems are the fastest growing technology. However, high PV penetration in the electricity grid is known to lead to numerous operational problems such as voltage fluctuations and line congestions, which could be eased by utilizing the reactive power capability of PV systems. To this end, we propose to use artificial neural network (ANN) to predict optimal reactive power dispatch in PV systems by learning approximate input–output mappings from AC optimal power flow (ACOPF) solutions in either a centralized or a decentralized manner. In the case of decentralized control, we leverage Shapley Additive Explanations (SHAP), an explainable artificial intelligence (XAI) technique, to identify non-local grid state measurements which significantly influence the optimal dispatch of each individual system. Both centralized and decentralized ANN-based controllers are evaluated through a case study based on the CIGRE medium-voltage distribution grid and compared to baseline control strategies. Results show that both ANN-based controllers exhibit superior performance, hindering voltage problems and line congestions which are encountered with baseline strategies while recording an energy saving of 0.44% compared to fixed power factor control. By leveraging ANN and SHAP, the proposed decentralized controllers for reactive power control are able to achieve ACOPF-level performance while promoting data privacy and reducing computational burden.

Monte Carlo simulation of SDEs using GANs

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ithat{text {o}} stochastic differential equations (SDEs). We propose a scheme that approximates the path-wise conditional distribution of SDEs for large time steps. Standard GANs are only able to approximate processes in distribution, yielding a weak approximation to the SDE. A conditional GAN architecture is proposed that enables strong approximation. We inform the discriminator of this GAN with the map between the prior input to the generator and the corresponding output samples, i.e. we introduce a ‘supervised GAN’. We compare the input-output map obtained with the standard GAN and supervised GAN and show experimentally that the standard GAN may fail to provide a path-wise approximation. The GAN is trained on a dataset obtained with exact simulation. The architecture was tested on geometric Brownian motion (GBM) and the Cox–Ingersoll–Ross (CIR) process. The supervised GAN outperformed the Euler and Milstein schemes in strong error on a discretisation with large time steps. It also outperformed the standard conditional GAN when approximating the conditional distribution. We also demonstrate how standard GANs may give rise to non-parsimonious input-output maps that are sensitive to perturbations, which motivates the need for constraints and regularisation on GAN generators.

PI control of stable nonlinear plants using projected dynamical systems

This paper presents a novel anti-windup proportional–integral controller for stable multi-input multi-output nonlinear plants. We use tools from projected dynamical systems theory to force the integrator state to remain in a desired (compact and convex) region, such that the plant input steady-state values satisfy the operational constraints of the problem. Under suitable monotonicity assumptions on the plant steady-state input–output map, we use singular perturbation theory results to prove the existence of a sufficiently small controller gain ensuring closed-loop (local) exponential stability and reference tracking for a feasible set of constant references. We suggest a particular controller design, which embeds (when possible) the right inverse of the plant steady-state input–output map. The relevance of the proposed controller scheme is validated through an application in the power systems domain, namely, the output (active and reactive) power regulation for a grid-connected synchronverter.

Development and comparison of artificial intelligence models for estimating daily reference evapotranspiration from limited input variables

The accurate and efficient computational modelling framework for computation of reference evapotranspiration (ET0) is the need of time and is highly essential for several agricultural, hydrological and hydro-climatological studies and applications. ET0 has its own role especially for the water resource system management including irrigation water allocation and management, utilization and demand assessments of water resources. Considering the potential and wide applicability of Artificial Intelligence (AI) models in input-output mapping, these were examined in this research for modelling ET0 utilising a variety of meteorological data, including maximum temperature (Tmax) and minimum temperature (Tmin), relative humidity (RH), wind speed (WS), and bright sunshine hours (BSS). The different AI models investigated in this study include Artificial Neural Network (ANN), Extreme Learning Machine (ELM), M5 Tree and Multiple Linear Regression (MLR). The implemented daily dataset was collected from the Sardarkrushinagar station which is located at the North Gujarat region of India. For performance verification of the developed AI models, the FAO-56 Penman-Monteith equation was employed as a benchmark. The developed model's accuracy was assessed using multiple quantitative metrics, including R2, NSE, RMSE, Pdv and MAE. The performance of ANN models was found better compared to the ELM, M5 Tree, and MLR models in terms of different performance indicators. The model's outcomes were highly practical and reliable for the investigated case studies. Another important finding in this research was that the selection of the appropriate input variables in models allows not only error minimization but also enhances the co-relationship amongst the dependant as well as independent variables.