The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization.

Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry, physically simulate solids, fluids, and other media, and render the world via optical techniques. These fine-tuned computations that operate explicitly on a given input solve so-called forward problems, VC excels at. By contrast, deep learning (DL) allows for the construction of general algorithmic models, side stepping the need for a purely first principles-based approach to problem solving. DL is powered by highly parameterized neural network architectures -- universal function approximators -- and gradient-based search algorithms which can efficiently search that large parameter space for optimal models. This approach is predicated by neural network differentiability, the requirement that analytic derivatives of a given problem's task metric can be computed with respect to neural network's parameters. Neural networks excel when an explicit model is not known, and neural network training solves an inverse problem in which a model is computed from data. While VC provides a strong inductive bias about the dynamics of realworld phenomena -- one that would otherwise have to be learned from scratch in a pure DL context -- its inability to adapt its mathematical models based on observations of real-world phenomena precludes its direct integration into larger DL-based systems.

To enable highly automated vehicles where the driver is no longer a safety backup, the vehicle must deal with various Functional Insufficiencies (FIs). Thus-far, there is no widely accepted functional architecture that maximizes the availability of autonomy and ensures safety in complex vehicle operational design domains. In this paper, we present a survey of existing methods that strive to prevent or handle FIs. We observe that current design-time methods of preventing FIs lack completeness guarantees. Complementary solutions for on-line handling cannot suitably increase safety without seriously impacting availability of journey continuing autonomous functionality. To fill this gap, we propose the Safety Shell, a scalable multi-channel architecture and arbitration design, built upon preexisting functional safety redundant channel architectures. We compare this novel approach to existing architectures using numerical case studies. The results show that the Safety Shell architecture allows the automated vehicle to be as safe or safer compared to alternatives, while simultaneously improving availability of vehicle autonomy, thereby increasing the possible coverage of on-line functional insufficiency handling.

We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-TH$\varepsilon$O POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-TH$\varepsilon$O POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Three key applications in finance and insurance are provided, namely, multi-period portfolio optimization, transfer learning in multi-period portfolio optimization, and insurance claim prediction, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-TH$\varepsilon$O POULA compared to SGLD, TUSLA, ADAM, and AMSGrad in terms of model accuracy.

Feedforward generalizable models for implicit shape reconstruction from unoriented point cloud present multiple advantages, including high performance and inference speed. However, they still suffer from generalization issues, ranging from underfitting the input point cloud, to misrepresenting samples outside of the training data distribution, or with toplogies unseen at training. We propose here an efficient mechanism to remedy some of these limitations at test time. We combine the inter-shape data prior of the network with an intra-shape regularization prior of a Nystr\"om Kernel Ridge Regression, that we further adapt by fitting its hyperprameters to the current shape. The resulting shape function defined in a shape specific Reproducing Kernel Hilbert Space benefits from desirable stability and efficiency properties and grants a shape adaptive expressiveness-robustness trade-off. We demonstrate the improvement obtained through our method with respect to baselines and the state-of-the-art using synthetic and real data.

This work proposes a novel data-driven model capable of providing accurate predictions for the power generation of all wind turbines in wind farms of arbitrary layout, yaw angle configurations and wind conditions. The proposed model functions by encoding a wind farm into a fully-connected graph and processing the graph representation through a graph transformer. The graph transformer surrogate is shown to generalise well and is able to uncover latent structural patterns within the graph representation of wind farms. It is demonstrated how the resulting surrogate model can be used to optimise yaw angle configurations using genetic algorithms, achieving similar levels of accuracy to industrially-standard wind farm simulation tools while only taking a fraction of the computational cost.

Understanding material surfaces and interfaces is vital in applications like catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can in principle predict the structure of material surfaces as a function of thermodynamic variables. However, accurate energy simulations are prohibitive when coupled to the vast phase space that must be statistically sampled. Here, we present a bi-faceted computational loop to predict surface phase diagrams of multi-component materials that accelerates both the energy scoring and statistical sampling methods. Fast, scalable, and data-efficient machine learning interatomic potentials are trained on high-throughput density-functional theory calculations through closed-loop active learning. Markov-chain Monte Carlo sampling in the semi-grand canonical ensemble is enabled by using virtual surface sites. The predicted surfaces for GaN(0001), Si(111), and SrTiO3(001) are in agreement with past work and suggest that the proposed strategy can model complex material surfaces and discover previously unreported surface terminations.

Safe and smooth motion control is essential for mobile robots when performing various automation tasks around obstacles, especially in the presence of people and other mobile robots. The total turning and space used by a mobile robot while moving towards a specified goal position play a crucial role in determining the required control effort and complexity. In this paper, we consider a standard unicycle control approach based on angular feedback linearization and provide an explicit analytical measure for determining the total turning effort during unicycle control in terms of unicycle state and control gains. We show that undesired spiral oscillatory motion around the goal position can be avoided by choosing a higher angular control gain compared to the linear control gain. Accordingly, we establish an accurate, explicit triangular motion range bound on the closed-loop unicycle trajectory using the total turning effort. The improved accuracy in motion range prediction results from a stronger dependency on the unicycle state and control parameters. To compare alternative circular, conic, and triangular motion range prediction approaches, we present an application of the proposed unicycle motion control and motion prediction methods for safe unicycle path following around obstacles in numerical simulations.

Sub-atomically focused electron beams in scanning transmission electron microscopes (STEMs) can induce a broad spectrum of chemical changes, including defect formation, reconfiguration of chemical bonds, and dopant insertion. Several groups have shown the feasibility of direct atomic manipulation via electron beam stimulation, which holds great promise for a number of downstream applications such as material design, solid-state quantum computers, and others (Jesse et al, 2018; Susi et al, 2017b; Dyck et al, 2017; Tripathi et al, 2018; Dyck et al, 2018). One of the challenges for advances in this space is that these types of atomic manipulation rely on manual control by highly-trained experts, which is expensive and slow. The ability to accurately automate this type of beam control could thereby result in tremendous impact on the feasibility of atomic manipulation for real use cases. A critical requirement for this automation is accurate estimation of the transition dynamics of atoms when stimulated by focused electron beams.

Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. Recent works show that decision quality can be improved in this setting by solving and differentiating the optimization problem in the training loop, enabling end-to-end training with loss functions defined directly on the resulting decisions. However, this approach can be inefficient and requires handcrafted, problem-specific rules for backpropagation through the optimization step. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient, accurate, and flexible solutions to an array of challenging Predict-Then-Optimize problems.