我们研究了仅当仅可用的嘈杂数据时，重建神经网络反问题的解决方案的问题。我们假设问题可以用无限可逆的无限前向操作员建模。然后，我们将该正向操作员限制为有限维空间，以使逆向Lipschitz连续。对于逆操作员，我们证明存在一个神经网络，该神经网络是操作员的健壮到噪声近似。此外，我们表明可以从适当的干扰培训数据中学到这些神经网络。我们证明了这种方法对实践感兴趣的各种反向问题的可接受性。给出了支持理论发现的数值示例。

A Digital Twin (DT) is a simulation of a physical system that provides information to make decisions that add economic, social or commercial value. The behaviour of a physical system changes over time, a DT must therefore be continually updated with data from the physical systems to reflect its changing behaviour. For resource-constrained systems, updating a DT is non-trivial because of challenges such as on-board learning and the off-board data transfer. This paper presents a framework for updating data-driven DTs of resource-constrained systems geared towards system health monitoring. The proposed solution consists of: (1) an on-board system running a light-weight DT allowing the prioritisation and parsimonious transfer of data generated by the physical system; and (2) off-board robust updating of the DT and detection of anomalous behaviours. Two case studies are considered using a production gas turbine engine system to demonstrate the digital representation accuracy for real-world, time-varying physical systems.

Training agents via off-policy deep reinforcement learning (RL) requires a large memory, named replay memory, that stores past experiences used for learning. These experiences are sampled, uniformly or non-uniformly, to create the batches used for training. When calculating the loss function, off-policy algorithms assume that all samples are of the same importance. In this paper, we hypothesize that training can be enhanced by assigning different importance for each experience based on their temporal-difference (TD) error directly in the training objective. We propose a novel method that introduces a weighting factor for each experience when calculating the loss function at the learning stage. In addition to improving convergence speed when used with uniform sampling, the method can be combined with prioritization methods for non-uniform sampling. Combining the proposed method with prioritization methods improves sampling efficiency while increasing the performance of TD-based off-policy RL algorithms. The effectiveness of the proposed method is demonstrated by experiments in six environments of the OpenAI Gym suite. The experimental results demonstrate that the proposed method achieves a 33%~76% reduction of convergence speed in three environments and an 11% increase in returns and a 3%~10% increase in success rate for other three environments.

We describe a Physics-Informed Neural Network (PINN) that simulates the flow induced by the astronomical tide in a synthetic port channel, with dimensions based on the Santos - S\~ao Vicente - Bertioga Estuarine System. PINN models aim to combine the knowledge of physical systems and data-driven machine learning models. This is done by training a neural network to minimize the residuals of the governing equations in sample points. In this work, our flow is governed by the Navier-Stokes equations with some approximations. There are two main novelties in this paper. First, we design our model to assume that the flow is periodic in time, which is not feasible in conventional simulation methods. Second, we evaluate the benefit of resampling the function evaluation points during training, which has a near zero computational cost and has been verified to improve the final model, especially for small batch sizes. Finally, we discuss some limitations of the approximations used in the Navier-Stokes equations regarding the modeling of turbulence and how it interacts with PINNs.

Models of sensory processing and learning in the cortex need to efficiently assign credit to synapses in all areas. In deep learning, a known solution is error backpropagation, which however requires biologically implausible weight transport from feed-forward to feedback paths. We introduce Phaseless Alignment Learning (PAL), a bio-plausible method to learn efficient feedback weights in layered cortical hierarchies. This is achieved by exploiting the noise naturally found in biophysical systems as an additional carrier of information. In our dynamical system, all weights are learned simultaneously with always-on plasticity and using only information locally available to the synapses. Our method is completely phase-free (no forward and backward passes or phased learning) and allows for efficient error propagation across multi-layer cortical hierarchies, while maintaining biologically plausible signal transport and learning. Our method is applicable to a wide class of models and improves on previously known biologically plausible ways of credit assignment: compared to random synaptic feedback, it can solve complex tasks with less neurons and learn more useful latent representations. We demonstrate this on various classification tasks using a cortical microcircuit model with prospective coding.

We introduce hp-greedy, a refinement approach for building gravitational wave surrogates as an extension of the standard reduced basis framework. Our proposal is data-driven, with a domain decomposition of the parameter space, local reduced basis, and a binary tree as the resulting structure, which are obtained in an automated way. When compared to the standard global reduced basis approach, the numerical simulations of our proposal show three salient features: i) representations of lower dimension with no loss of accuracy, ii) a significantly higher accuracy for a fixed maximum dimensionality of the basis, in some cases by orders of magnitude, and iii) results that depend on the reduced basis seed choice used by the refinement algorithm. We first illustrate the key parts of our approach with a toy model and then present a more realistic use case of gravitational waves emitted by the collision of two spinning, non-precessing black holes. We discuss performance aspects of hp-greedy, such as overfitting with respect to the depth of the tree structure, and other hyperparameter dependences. As two direct applications of the proposed hp-greedy refinement, we envision: i) a further acceleration of statistical inference, which might be complementary to focused reduced-order quadratures, and ii) the search of gravitational waves through clustering and nearest neighbors.

Most TextVQA approaches focus on the integration of objects, scene texts and question words by a simple transformer encoder. But this fails to capture the semantic relations between different modalities. The paper proposes a Scene Graph based co-Attention Network (SceneGATE) for TextVQA, which reveals the semantic relations among the objects, Optical Character Recognition (OCR) tokens and the question words. It is achieved by a TextVQA-based scene graph that discovers the underlying semantics of an image. We created a guided-attention module to capture the intra-modal interplay between the language and the vision as a guidance for inter-modal interactions. To make explicit teaching of the relations between the two modalities, we proposed and integrated two attention modules, namely a scene graph-based semantic relation-aware attention and a positional relation-aware attention. We conducted extensive experiments on two benchmark datasets, Text-VQA and ST-VQA. It is shown that our SceneGATE method outperformed existing ones because of the scene graph and its attention modules.

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al. (ICLR 2021), which exhibit startling new phenomena (the "edge of stability" or "unstable convergence") and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks. For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons (i.e., neurons with a non-zero first-layer bias). This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

Generative Adversarial Networks (GANs) were introduced by Goodfellow in 2014, and since then have become popular for constructing generative artificial intelligence models. However, the drawbacks of such networks are numerous, like their longer training times, their sensitivity to hyperparameter tuning, several types of loss and optimization functions and other difficulties like mode collapse. Current applications of GANs include generating photo-realistic human faces, animals and objects. However, I wanted to explore the artistic ability of GANs in more detail, by using existing models and learning from them. This dissertation covers the basics of neural networks and works its way up to the particular aspects of GANs, together with experimentation and modification of existing available models, from least complex to most. The intention is to see if state of the art GANs (specifically StyleGAN2) can generate album art covers and if it is possible to tailor them by genre. This was attempted by first familiarizing myself with 3 existing GANs architectures, including the state of the art StyleGAN2. The StyleGAN2 code was used to train a model with a dataset containing 80K album cover images, then used to style images by picking curated images and mixing their styles.

Modern machine learning pipelines are limited due to data availability, storage quotas, privacy regulations, and expensive annotation processes. These constraints make it difficult or impossible to maintain a large-scale model trained on growing annotation sets. Continual learning directly approaches this problem, with the ultimate goal of devising methods where a neural network effectively learns relevant patterns for new (unseen) classes without significantly altering its performance on previously learned ones. In this paper, we address the problem of continual learning for video data. We introduce PIVOT, a novel method that leverages the extensive knowledge in pre-trained models from the image domain, thereby reducing the number of trainable parameters and the associated forgetting. Unlike previous methods, ours is the first approach that effectively uses prompting mechanisms for continual learning without any in-domain pre-training. Our experiments show that PIVOT improves state-of-the-art methods by a significant 27% on the 20-task ActivityNet setup.