Input-output Mapping Research Articles

Addition and intersection of linear time-invariant behaviors

We define and analyze the operations of addition and intersection of linear time-invariant systems in the behavioral setting, where systems are viewed as sets of trajectories rather than input–output maps. The classical definition of addition of input–output systems is addition of the outputs with the inputs being equal. In the behavioral setting, addition of systems is defined as addition of all variables. Intersection of linear time-invariant systems was considered before only for the autonomous case in the context of “common dynamics” estimation. We generalize the notion of common dynamics to open systems (systems with inputs) as intersection of behaviors. This is done by proposing trajectory-based definitions. The main results of the paper are (1) characterization of the link between the complexities (number of inputs and order) of the sum and intersection systems, (2) algorithms for computing their kernel and image representations and (3) a duality property of the two operations. Our approach combines polynomial and numerical linear algebra computations.

Explainable machine learning for hydrocarbon prospect risking

Hydrocarbon prospect risk assessment is an important process in oil and gas exploration involving the integrated analysis of various geophysical data modalities, including seismic data, well logs, and geologic information, to estimate the likelihood of drilling success for a given drill location. Over the years, geophysicists have attempted to understand the various factors at play influencing the probability of success for hydrocarbon prospects. Toward this end, a large database of prospect drill outcomes and associated attributes has been collected and analyzed via correlation-based techniques to determine the features that contribute the most in deciding the final outcome. Machine learning (ML) has the potential to model complex feature interactions to learn input-output mappings for complicated high-dimensional data sets. However, in many instances, ML models are not interpretable to end users, limiting their utility toward understanding the underlying scientific principles for the problem domain and being deployed to assist in the risk assessment process. In this context, we leverage the concept of explainable ML to interpret various black-box ML models trained on the aforementioned prospect database for risk assessment. Using various case studies on real data, we determine that this model-agnostic explainability analysis for prospect risking can (1) reveal novel scientific insights into the interplay of various features in regard to deciding prospect outcome, (2) assist with performing feature engineering for ML models, (3) detect bias in data sets involving spurious correlations, and (4) build a global picture of a model’s understanding of the data by aggregating local explanations on individual data points.

An inverse source time-fractional diffusion problem via an input-output mapping

In this paper, we investigate an inverse source problem involving a one-dimensional diffusion equation of a time-fractional RiemannLiouville derivative with 0 < α < 1. First, results on the existence and regularity of the weak solution of the direct problem are obtained. For the determination of the unknown time-dependent source term, we use a monotone and distinguishable input-output mapping defined by the additional over-determination integral data for the considered sub-diffusion problem. Finally, the uniqueness of the solution of the inverse problem is proved.

Stock Market Trend Analysis and Machine Learning-based Predictive Evaluation

Financial experts may make successful selections thanks to the stock market's research and forecasting capabilities, which is exciting. This study examines the stock market forecast outcomes through a simple feed-forward neural network (FFNN) model. Then, we contrast those outcomes with those produced using more sophisticated Elman, fuzzy logic, and radial basis function networks. Any problem with finite input-output mapping may be solved using the FFNN as long as it has at least one hidden layer and a sufficient number of neurons. An ANN in which RBFs are used as activation functions is called a radial basis function network (RBFN). Utilizing the Levenberg-Marquardt Back Propagation technique, the FFNN and Elman networks are trained in this study. A Fuzzy Inference System (FIS) of Sugeno type is employed to replicate the predictive procedure within the realm of fuzzy logic. We choose the optimal RBF values using several clustering techniques. The approaches were validated using public stock market data on the National Stock Exchange of Indonesia.

Anatomical Connectivity of the Intercalated Cells of the Amygdala.

The intercalated cells of the amygdala (ITCs) are a fundamental processing structure in the amygdala that remain relatively understudied. They are phylogenetically conserved from insectivores through primates, inhibitory, and project to several of the main processing and output stations of the amygdala and basal forebrain. Through these connections, the ITCs are best known for their role in conditioned fear, where they are required for fear extinction learning and recall. Prior work on ITC connectivity is limited, and thus holistic characterization of their afferent and efferent connectivity in a genetically defined manner is incomplete. The ITCs express the FoxP2 transcription factor, affording genetic access to these neurons for viral input-output mapping. To fully characterize the anatomic connectivity of the ITCs, we used cre-dependent viral strategies in FoxP2-cre mice to reveal the projections of the main (mITC), caudal (cITC), and lateral (lITC) clusters along with their presynaptic sources of innervation. Broadly, the results confirm many known pathways, reveal previously unknown ones, and demonstrate important novel insights about each nucleus's unique connectivity profile and relative distributions. We show that the ITCs receive information from a wide range of cortical, subcortical, basal, amygdalar, hippocampal, and thalamic structures, and project broadly to areas of the basal forebrain, hypothalamus, and entire extent of the amygdala. The results provide a comprehensive map of their connectivity and suggest that the ITCs could potentially influence a broad range of behaviors by integrating information from a wide array of sources throughout the brain.

Three-mirror free-form off-axis antenna design of beam shaping on a circular substrate

This work presents a design of a three-mirror free-form surface beam shaping system with small dimensions, easy assembly, and good collimation. To facilitate integration and assembly, the three mirrors are integrated into a circular substrate with a radius of 90 mm. Based on the law of energy conservation, Fermat’s principle, and the vector theory of reflection, the input–output mapping is derived, and the three free-form mirrors are constructed point by point simultaneously. Ray tracing results demonstrate that the maximum divergence angle is compressed to 0.467 mrad and the standard deviation of the edge beam radius samples (SDRS) is reduced from 5.42mm to 0.985mm on the receiving plane. The light intensity has a relative root mean square deviation (RRMSD) of only 0.049. Furthermore, the results show that the minimum value of SDRS is 0.940mm at a propagation distance of L=1.72 m, while the minimum value of RRMSD is 0.0431 at L=7.03 m. In addition, the effects of astigmatism and light source offsets on the collimated and shaping effect are analyzed. The design of the free-form surfaces antenna system in this work will provide a new design method for practical engineering and application, and will greatly improve the quality and propagation distance of the Gaussian beam.

Machine learning prediction of structural dynamic responses using graph neural networks

Prediction of structural responses is essential for the analysis of structural behaviour subjected to dynamic loads. Existing approaches are limited in different ways. Experimental tests are expensive due to the requirement of intensive labour hours and specialised equipment. Numerical models can provide high-fidelity and labour-effective simulation of impact tests after proper validation, but it comes with high computational costs, which prohibit the usage of numerical methods for intensive and large-scale simulations in a design office. Data-driven machine learning approaches are also applied to structural response predictions, but they often exploit direct input–output mapping schemes that predict static field variables without capturing the dynamic response process. To close these gaps, we propose a novel machine learning approach based on graph neural networks (GNN) for full-field structural dynamics prediction. Our approach adopts a discretised representation of structures with an iterative rollout prediction scheme, and therefore it can simulate comprehensive spatiotemporal structural dynamics, providing the full potential for structural dynamics analysis. With several benchmark tests, it is demonstrated that our approach can generate accurate predictions of related field variables, e.g., displacement, strain, and stress, for different structures with a wide range of input parameters, such as structure geometry, impact speed and location. Additional interpolation and extrapolation tests are also conducted to show that our approach enjoys inherent generalisability and can produce satisfactory prediction even when all inputs are sampled outside of the training distribution. Our approach is also efficient and runs an order of magnitude faster than the commonly used numerical competitors. As the first attempt of using GNN for structural dynamics prediction and the result is promising, it is believed that GNN is well-suited for effective and efficient prediction of dynamic structural responses.

A Hybrid Theory-Driven and Data-Driven Modeling Method for Solving the Shallow Water Equations

In recent years, mountainous areas in China have faced frequent geological hazards, including landslides, debris flows, and collapses. Effective simulation of these events requires a solver for shallow water equations (SWEs). Traditional numerical methods, such as finite difference and finite volume, face challenges in discretizing convection flux terms, while theory-based models need to account for various factors such as shock wave capturing and wave propagation direction, demanding a high-level understanding of the underlying physics. Previous deep learning (DL)-based SWE solvers primarily focused on constructing direct input–output mappings, leading to weak generalization properties when terrain data or stress constitutive relations change. To overcome these limitations, this study introduces a novel SWE solver that combines theory and data-driven methodologies. The core idea is to use artificial neural networks to compute convection flux terms, and to reduce modeling complexity. Theory-based modeling is used to tackle complex terrain and friction terms for the purpose of ensuring generalization. Our method surpasses challenges faced by previous DL-based solvers in capturing terrain and stress variations. We validated our solver’s capabilities by comparing simulation results with analytical solutions, real-world disaster cases, and the widely used Massflow software-generated simulations. This comprehensive comparison confirms our solver’s ability to accurately simulate hazard scenarios and showcases strong generalization on varying terrain and land surface friction. Our proposed method effectively addresses DL-based solver limitations while simplifying the complexities of theory-driven numerical methods, offering a promising approach for hazard dynamics simulation.

A surrogate modeling method for distributed land surface hydrological models based on deep learning

Surrogate modelling methods have been used to estimate spatially distributed parameters of land surface hydrological models due to their computational efficiency. However, traditional surrogate techniques have trouble in modelling high-dimensional input–output maps. In addition, their applications to a distributed model over large spatial and temporal domains are very unlikely to produce consistent spatial pattern and dynamic relationship of model input and output, leading to unbalanced model performance across different spatiotemporal domains. To address these issues, we employ a deep autoregressive neural network to construct an accurate and reliable surrogate system of distributed dynamic model outputs. The network uses a deep convolutional encoder-decoder architecture to take full advantage of the deep convolutional layers in high-dimensional image processing and spatial feature extraction. Moreover, the autoregressive strategy makes the network good at handling dynamic relationship between the time-varying model input and output. We apply this deep learning (DL) network to building a surrogate model of the Variable Infiltration Capacity (VIC) model simulated soil moisture over the Huaihe river basin of China. The results show that the adopted deep autoregressive neural network can provide an accurate surrogate model of the high-dimensional dynamic relationship between 15 input fields and 1 output field, each covering 408 grids, over multiple years. This surrogate model significantly outperforms the popular long short-term memory (LSTM) model, achieving an average mean squared error (MSE) of 0.26 and an average R2 of 0.76 using the test datasets. The surrogate's MSE and R2 performance represents an average improvement of 43% and 33%, respectively, compared to the LSTM model. In addition, it shows better spatial performance than the LSTM model, demonstrating its superior performance in approximating spatial patterns of VIC simulated soil moisture. The accuracy of this surrogate method and its ability to handle high-dimensional data is promising for advancing parameter uncertainty quantification of distributed land surface hydrological models, which usually have high dimensionality due to the large number of variables involved, including distributed parameters, input forcing variables, and output variables.

Security Threat Mitigation for Smart Contracts: A Comprehensive Survey

The blockchain technology, initially created for cryptocurrency, has been re-purposed for recording state transitions of smart contracts—decentralized applications that can be invoked through external transactions. Smart contracts gained popularity and accrued hundreds of billions of dollars in market capitalization in recent years. Unfortunately, like all other computer programs, smart contracts are prone to security vulnerabilities that have incurred multibillion-dollar damages over the past decade. As a result, many automated threat mitigation solutions have been proposed to counter the security issues of smart contracts. These threat mitigation solutions include various tools and methods that are challenging to compare. This survey develops a comprehensive classification taxonomy of smart contract threat mitigation solutions within five orthogonal dimensions: defense modality, core method, targeted contracts, input-output data mapping, and threat model. We classify 133 existing threat mitigation solutions using our taxonomy and confirm that the proposed five dimensions allow us to concisely and accurately describe any smart contract threat mitigation solution. In addition to learning what the threat mitigation solutions do, we also show how these solutions work by synthesizing their actual designs into a set of uniform workflows corresponding to the eight existing defense core methods. We further create an integrated coverage map for the known smart contract vulnerabilities by the existing threat mitigation solutions. Finally, we perform the evidence-based evolutionary analysis, in which we identify trends and future perspectives of threat mitigation in smart contracts and pinpoint major weaknesses of the existing methodologies. For the convenience of smart contract security developers, auditors, users, and researchers, we deploy and maintain a regularly updated comprehensive open-source online registry of threat mitigation solutions, called Security Threat Mitigation (STM) Registry at https://seit.egr.msu.edu/research/stmregistry/ .

A dimensionality reduction approach for convolutional neural networks

The focus of this work is on the application of classical Model Order Reduction techniques, such as Active Subspaces and Proper Orthogonal Decomposition, to Deep Neural Networks. We propose a generic methodology to reduce the number of layers in a pre-trained network by combining the aforementioned techniques for dimensionality reduction with input-output mappings, such as Polynomial Chaos Expansion and Feedforward Neural Networks. The motivation behind compressing the architecture of an existing Convolutional Neural Network arises from its usage in embedded systems with specific storage constraints. The conducted numerical tests demonstrate that the resulting reduced networks can achieve a level of accuracy comparable to the original Convolutional Neural Network being examined, while also saving memory allocation. Our primary emphasis lies in the field of image recognition, where we tested our methodology using VGG-16 and ResNet-110 architectures against three different datasets: CIFAR-10, CIFAR-100, and a custom dataset.

Modelling opacity and variation in Gran Canarian Spanish apocope

In this paper, we present novel data from Spanish spoken on Gran Canaria which show an interaction of two lenition processes: final consonant deletion and vowel apocope. We show that in certain positions in an utterance, these processes optionally combine in a fed counterfeeding interaction. Furthermore, the variation present in the dialect due to process optionality uncovers a latent opacity pattern, i.e. an additional opaque interaction that is not motivated by any individual input-output mapping, but only by the quantitative aspect of variation. This takes the form of mutual counterfeeding, a rarely reported phenomenon, thus creating a novel test case for theories of opacity. The second part of the paper provides a formal analysis of the opacity-ridden data, taking into account process optionality and variation. The theoretical analysis and learning simulations using the Expectation-Driven Learner demonstrate that a probabilistic variant of Serial Markedness Reduction can capture both fed counterfeeding and latent opacity without recourse to additional mechanisms beyond the original framework, as opposed to analyses in other serial frameworks such as OT-CC. Our analysis shows that opacity with optional processes is a complex problem that has to be specifically addressed with probabilistic frameworks.

Robust nonlinear decision mapping approach for online bus speed control under uncertainty

AbstractThe degradation of bus system attractiveness is primarily caused by low‐level service quality and reliability. As an essential technology for bus operation management, online bus speed control has proven to be a flexible and effective solution to mitigate bus bunching and enhance the service level of bus operation systems. In this study, we propose a robust nonlinear decision mapping (RNDM) approach that uses real‐time key bus system states to control bus speeds and accounts for uncertainties associated with passenger demands at stations and traffic speeds of interstation links. We develop this approach through a design process that involves learning the input–output mapping relation of a nonlinear programming simulation‐based optimization (NLPSO) method using regression tree with AdaBoost. Critical parameters of the fitted regression tree with AdaBoost are then optimized offline using a distributionally robust simulation‐based optimization (DRSO) model that is solved by a simulation‐based optimization (SO) algorithm. The resulting RNDM method effectively handles two types of uncertainties, expressed by two ambiguity sets of probability distributions, and ensures good bus operation performance even under worst‐case uncertainty levels. Numerical experiments reveal that the RNDM, NLPSO, and integer programming SO (IPSO) methods successfully mitigate bus bunching and improve service efficiency and robustness, compared to the no‐control scenario. Furthermore, the RNDM method outperforms NLPSO and IPSO in terms of comprehensive performance under uncertainties and demonstrates practical operability. In conclusion, this study presents an innovative general framework that uses a nonlinear decision mapping optimized offline by an SO approach to address online simulation‐based optimal decision‐making problems under uncertainties, which can be applied to solve similar problems.

Optimal coordinated congestion pricing for multiple regions: a surrogate-based approach

Congestion pricing is one of the efficient travel demand management strategies. Many existing researches focus on dealing with the toll optimization problem for a single area. However, the urban network is often composed of several administrative regions. Furthermore, even inside a single administrative region, there may be multiple subnetworks with different traffic dynamics. As a result, the centric pricing scheme may not be applicable. This paper aims to design a coordinated dynamic pricing scheme for such a scenario with multiple adjacent areas which experience an overlapping congested period. Unlike the traditional approach centered on the bi-level mathematical programming, we adopt the regressing Kriging model to estimate the input–output mapping, thus searching for the simulation-based optimal solution in the toll design problem. Two types of coordinated pricing schemes are proposed. The first or unconstrained scheme only focuses on the network performance, while the second or constrained scheme further takes into account the pricing efficiency. The proposed coordinated pricing scheme is further compared with the perimeter control. The results indicate that our scheme is more moderate without imposing traffic burden on the links/corridors heading to protected zones.

Spelling-sound consistency influences second-language age of acquisition effect: evidence for the arbitrary mapping hypothesis

ABSTRACT The age at which people acquire a word influences word recognition, known as the age of acquisition (AoA) effect. In the first language (L1), AoA effects are widely found in various languages and experimental tasks. Arbitrary Mapping Hypothesis proposes that AoA effects reflect the loss of network plasticity during the learning of mappings between input and output representations. It predicts that the AoA effect appears (or is larger) when the input-output mapping is arbitrary/inconsistent, relative to consistent input-output mapping. The present study examined how these predictions generalised to the second language (L2). We explored whether the L2 AoA effect was modulated by spelling-sound consistency in Chinese-English bilinguals, adopting a delayed word naming task. The results showed that the mapping consistency modulated the L2 AoA effect on the N170, P200 and N400 components. L2 AoA effect was insignificant in the consistent condition but was significant in the inconsistent condition: late-acquired words elicited larger N170, smaller P200, and larger N400 compared to early-acquired words. These findings suggest that L2 AoA effects occur in the spelling-sound connections, providing direct evidence for the Arbitrary Mapping Hypothesis.

Computing in the nick of time

AbstractThe medium‐independence of computational descriptions has shaped common conceptions of computational explanation. So long as our goal is to explain how a system successfully carries out its computations, then we only need to describe the abstract series of operations that achieve the desired input–output mapping, however they may be implemented. It is argued that this abstract conception of computational explanation cannot be applied to so‐called real‐time computing systems, in which meeting temporal deadlines imposed by the systems with which a device interfaces are constitutive of the computing tasks that a device performs. Instead, real‐time computing reveals the need for alternative conceptions of computational explanation, as well as computational implementation, that eschew medium‐independence.

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Developing new ways to estimate probabilities can be valuable for science, statistics, engineering, and other fields. By considering the information content of different output patterns, recent work invoking algorithmic information theory inspired arguments has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here, we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real-world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam’s razor, machine learning, and password guessing.

A New Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs

We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model, reduced order model (ROM), and machine learning (ML) model chain. The model is adaptive in the sense that the ROM and ML model are adapted on the fly during a sequence of parametric requests to the model. To allow for a certification of the model hierarchy, as well as to control the adaptation process, we employ rigorous a posteriori error estimates for the ROM and ML models. In particular, we provide an example of an ML-based model that allows for rigorous analytical quality statements. We demonstrate the efficiency of the modeling chain on a Monte Carlo and a parameter-optimization example. Here, the ROM is instantiated by Reduced Basis methods, and the ML model is given by a neural network or by a kernel model using vectorial kernel orthogonal greedy algorithms.

Data-Driven Inference on Optimal Input–Output Properties of Polynomial Systems With Focus on Nonlinearity Measures

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to determine nonlinearity measures and other optimal input-output properties for nonlinear polynomial systems without explicitly identifying a model but from a finite number of input-state measurements which are subject to noise. To this end, we deduce from data for the unidentified ground-truth system three possible set-membership representations, compare their accuracy, and prove that they are asymptotically consistent with respect to the amount of samples. Moreover, we leverage these representations to compute guaranteed upper bounds on nonlinearity measures and the corresponding optimal linear approximation model via semi-definite programming. Furthermore, we extend the established framework to determine optimal input-output properties described by time domain hard integral quadratic constraints.

A Novel Hybrid Intelligent SOPDEL Model with Comprehensive Data Preprocessing for Long-Time-Series Climate Prediction

Long-time-series climate prediction is of great significance for mitigating disasters; promoting ecological civilization; identifying climate change patterns and preventing floods, drought and typhoons. However, the general public often struggles with the complexity and extensive temporal range of meteorological data when attempting to accurately forecast climate extremes. Sequence disorder, weak robustness, low characteristics and weak interpretability are four prevalent shortcomings in predicting long-time-series data. In order to resolve these deficiencies, our study gives a novel hybrid spatiotemporal model which offers comprehensive data preprocessing techniques, focusing on data decomposition, feature extraction and dimensionality upgrading. This model provides a feasible solution to the puzzling problem of long-term climate prediction. Firstly, we put forward a Period Division Region Segmentation Property Extraction (PD-RS-PE) approach, which divides the data into a stationary series (SS) for an Extreme Learning Machine (ELM) prediction and an oscillatory series (OS) for a Long Short-term Memory (LSTM) prediction to accommodate the changing trend of data sequences. Secondly, a new type of input-output mapping mode in a three-dimensional matrix was constructed to enhance the robustness of the prediction. Thirdly, we implemented a multi-layer technique to extract features of high-speed input data based on a Deep Belief Network (DBN) and Particle Swarm Optimization (PSO) for parameter searching of a neural network, thereby enhancing the overall system’s learning ability. Consequently, by integrating all the above innovative technologies, a novel hybrid SS-OS-PSO-DBN-ELM-LSTME (SOPDEL) model with comprehensive data preprocessing was established to improve the quality of long-time-series forecasting. Five models featuring partial enhancements are discussed in this paper and three state-of-the-art classical models were utilized for comparative experiments. The results demonstrated that the majority of evaluation indices exhibit a significant optimization in the proposed model. Additionally, a relevant evaluation system showed that the quality of “Excellent Prediction” and “Good Prediction” exceeds 90%, and no data with “Bad Prediction” appear, so the accuracy of the prediction process is obviously insured.