Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in data-driven modeling techniques, in particular neural networks have proven to provide an effective framework for solving a wide range of tasks. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.

Are intelligent machines really intelligent? Is the underlying philosophical concept of intelligence satisfactory for describing how the present systems work? Is understanding a necessary and sufficient condition for intelligence? If a machine could understand, should we attribute subjectivity to it? This paper addresses the problem of deciding whether the so-called "intelligent machines" are capable of understanding, instead of merely processing signs. It deals with the relationship between syntaxis and semantics. The main thesis concerns the inevitability of semantics for any discussion about the possibility of building conscious machines, condensed into the following two tenets: "If a machine is capable of understanding (in the strong sense), then it must be capable of combining rules and intuitions"; "If semantics cannot be reduced to syntaxis, then a machine cannot understand." Our conclusion states that it is not necessary to attribute understanding to a machine in order to explain its exhibited "intelligent" behavior; a merely syntactic and mechanistic approach to intelligence as a task-solving tool suffices to justify the range of operations that it can display in the current state of technological development.

We study the performance -- and specifically the rate at which the error probability converges to zero -- of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $\sim \exp\left(-n\,I + o(n) \right)$, where $n$ is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and $I$ is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and, consequently, the related error rate $I$, depend on the given training set, which is assumed of finite size. Interestingly, these conditions can be verified and tested numerically exploiting the available dataset, or a synthetic dataset, generated according to the available information on the underlying statistical model. In other words, the classification error probability convergence to zero and its rate can be computed on a portion of the dataset available for training. Coherently with the large deviations theory, we can also establish the convergence, for $n$ large enough, of the normalized D3F statistic to a Gaussian distribution. This property is exploited to set a desired asymptotic false alarm probability, which empirically turns out to be accurate even for quite realistic values of $n$. Furthermore, approximate error probability curves $\sim \zeta_n \exp\left(-n\,I \right)$ are provided, thanks to the refined asymptotic derivation (often referred to as exact asymptotics), where $\zeta_n$ represents the most representative sub-exponential terms of the error probabilities.

This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside some ranges of interest: the mean of the predictive distributions no longer necessarily interpolates the observed values when they are outside ranges of interest, but are simply constrained to remain outside. This method called relaxed Gaussian process (reGP) interpolation provides better predictive distributions in ranges of interest, especially in cases where a stationarity assumption for the GP model is not appropriate. It can be viewed as a goal-oriented method and becomes particularly interesting in Bayesian optimization, for example, for the minimization of an objective function, where good predictive distributions for low function values are important. When the expected improvement criterion and reGP are used for sequentially choosing evaluation points, the convergence of the resulting optimization algorithm is theoretically guaranteed (provided that the function to be optimized lies in the reproducing kernel Hilbert spaces attached to the known covariance of the underlying Gaussian process). Experiments indicate that using reGP instead of stationary GP models in Bayesian optimization is beneficial.

Abstract: Traffic prediction plays an important role in the realization of traffic control and scheduling tasks in intelligent transportation systems. With the diversification of data sources, re asonably using rich traffic data to model the complex spatial-temporal dependence and nonlinear characteristics in traffic flow are the key challenge for intelligent transportation system. In addition, clearly evaluating the importance of spatialtemporal features extracted from different data becomes a challenge. A Double Layer - Spatial Temporal Feature Extraction and Evaluation (DL-STFEE) model is proposed. The lower layer of DL-STFEE is spatialtemporal feature extraction layer. The spatial and temporal features in traffic data are extracted by multi-graph graph convolution and attention mechanism, and different combinations of spatial and temporal features are generated. The upper layer of DL-STFEE is the spatial-temporal feature evaluation layer. Through the attention score matrix generated by the high-dimensional self-attention mechanism, the spatial-temporal features combinations are fused and evaluated, so as to get the impact of different combinations on prediction effect. Three sets of experiments are performed on actual traffic datasets to show that DL-STFEE can effectively capture the spatial-temporal features and evaluate the importance of different spatial-temporal feature combinations. With the continuous acceleration of urbanization, the population and vehicle ownership are also increasing, resulting in traffic congestion and other problems. In order to improve the efficiency, sustainability and security of transportation network, intelligent transportation system (ITS) [1] is proposed and becomes an advancing research field. Traffic prediction is an important step in the development of intelligent transportation [2]. It 2 aims to predict future traffic conditions by integrating historical observation data and measurement information of road sensor networks.

In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be efficiently learned via score matching, and used to flexibly generate credible samples to enhance discriminative classification quality, to recover density and to build generative classifiers. We analysed the decision theories involving score-based representations, and performed experiments on simulated and real-world datasets, demonstrating its effectiveness in achieving and improving binary classification performance, and robustness to perturbations, particularly in high dimensions and imbalanced situations.

Closed-loop reservoir management (CLRM), in which history matching and production optimization are performed multiple times over the life of an asset, can provide significant improvement in the specified objective. These procedures are computationally expensive due to the large number of flow simulations required for data assimilation and optimization. Existing CLRM procedures are applied asset by asset, without utilizing information that could be useful over a range assets. Here, we develop a CLRM framework for multiple assets with varying numbers of wells. We use deep reinforcement learning to train a single global control policy that is applicable for all assets considered. The new framework is an extension of a recently introduced control policy methodology for individual assets. Embedding layers are incorporated into the representation to handle the different numbers of decision variables that arise for the different assets. Because the global control policy learns a unified representation of useful features from multiple assets, it is less expensive to construct than asset-by-asset training (we observe about 3x speedup in our examples). The production optimization problem includes a relative-change constraint on the well settings, which renders the results suitable for practical use. We apply the multi-asset CLRM framework to 2D and 3D water-flooding examples. In both cases, four assets with different well counts, well configurations, and geostatistical descriptions are considered. Numerical experiments demonstrate that the global control policy provides objective function values, for both the 2D and 3D cases, that are nearly identical to those from control policies trained individually for each asset. This promising finding suggests that multi-asset CLRM may indeed represent a viable practical strategy.

Large language models (LMs) such as GPT-3 have the surprising ability to do in-context learning, where the model learns to do a downstream task simply by conditioning on a prompt consisting of input-output examples. The LM learns from these examples without being explicitly pretrained to learn. Thus, it is unclear what enables in-context learning. In this paper, we study how in-context learning can emerge when pretraining documents have long-range coherence. Here, the LM must infer a latent document-level concept to generate coherent next tokens during pretraining. At test time, in-context learning occurs when the LM also infers a shared latent concept between examples in a prompt. We prove when this occurs despite a distribution mismatch between prompts and pretraining data in a setting where the pretraining distribution is a mixture of HMMs. In contrast to messy large-scale datasets used to train LMs capable of in-context learning, we generate a small-scale synthetic dataset (GINC) where Transformers and LSTMs both exhibit in-context learning. Beyond the theory, experiments on GINC exhibit large-scale real-world phenomena including improved in-context performance with model scaling (despite the same pretraining loss), sensitivity to example order, and instances where zero-shot is better than few-shot in-context learning.

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs leads to a large possible topology candidate space, which often cannot be exhaustively searched due to the limitation in computational resources. This paper develops a scalable and efficient topology inference for GRNs using Bayesian optimization and kernel-based methods. Rather than an exhaustive search over possible topologies, the proposed method constructs a Gaussian Process (GP) with a topology-inspired kernel function to account for correlation in the likelihood function. Then, using the posterior distribution of the GP model, the Bayesian optimization efficiently searches for the topology with the highest likelihood value by optimally balancing between exploration and exploitation. The performance of the proposed method is demonstrated through comprehensive numerical experiments using a well-known mammalian cell-cycle network.

Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning frameworks, while retaining a probabilistic interpretation from the direct correspondence with hidden Markov models. Whilst the contribution is mainly theoretical, experiments on speech recognition indicate that adding the derived units at the end of state-of-the-art recurrent architectures can improve the performance at a very low cost in terms of trainable parameters.