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Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an end-to-end differentiable solver is used in combination with physics-inspired choices of deep learning architectures to learn highly effective and versatile SGS models for two-dimensional turbulent flow. We perform an in-depth analysis of the inductive biases in the chosen architectures, finding that the inclusion of small-scale non-local features is most critical to effective SGS modeling, while large-scale features can improve pointwise accuracy of the a-posteriori solution field. The filtered velocity gradient tensor can be mapped directly to the SGS stress via decomposition of the inputs and outputs into isotropic, deviatoric, and anti-symmetric components. We see that the model can generalize to a variety of flow configurations, including higher and lower Reynolds numbers and different forcing conditions. We show that the differentiable physics paradigm is more successful than offline, a-priori learning, and that hybrid solver-in-the-loop approaches to deep learning offer an ideal balance between computational efficiency, accuracy, and generalization. Our experiments provide physics-based recommendations for deep-learning based SGS modeling for generalizable closure modeling of turbulence.

Offline reinforcement learning (RL) is challenged by the distributional shift problem. To address this problem, existing works mainly focus on designing sophisticated policy constraints between the learned policy and the behavior policy. However, these constraints are applied equally to well-performing and inferior actions through uniform sampling, which might negatively affect the learned policy. To alleviate this issue, we propose Offline Prioritized Experience Replay (OPER), featuring a class of priority functions designed to prioritize highly-rewarding transitions, making them more frequently visited during training. Through theoretical analysis, we show that this class of priority functions induce an improved behavior policy, and when constrained to this improved policy, a policy-constrained offline RL algorithm is likely to yield a better solution. We develop two practical strategies to obtain priority weights by estimating advantages based on a fitted value network (OPER-A) or utilizing trajectory returns (OPER-R) for quick computation. OPER is a plug-and-play component for offline RL algorithms. As case studies, we evaluate OPER on five different algorithms, including BC, TD3+BC, Onestep RL, CQL, and IQL. Extensive experiments demonstrate that both OPER-A and OPER-R significantly improve the performance for all baseline methods. Codes and priority weights are availiable at //github.com/sail-sg/OPER.

Algorithmic differentiation (AD) is a set of techniques that provide partial derivatives of computer-implemented functions. Such a function can be supplied to state-of-the-art AD tools via its source code, or via an intermediate representation produced while compiling its source code. We present the novel AD tool Derivgrind, which augments the machine code of compiled programs with forward-mode AD logic. Derivgrind leverages the Valgrind instrumentation framework for a structured access to the machine code, and a shadow memory tool to store dot values. Access to the source code is required at most for the files in which input and output variables are defined. Derivgrind's versatility comes at the price of scaling the run-time by a factor between 30 and 75, measured on a benchmark based on a numerical solver for a partial differential equation. Results of our extensive regression test suite indicate that Derivgrind produces correct results on GCC- and Clang-compiled programs, including a Python interpreter, with a small number of exceptions. While we provide a list of scenarios that Derivgrind does not handle correctly, nearly all of them are academic counterexamples or originate from highly optimized math libraries. As long as differentiating those is avoided, Derivgrind can be applied to an unprecedentedly wide range of cross-language or partially closed-source software with little integration efforts.

Human beings cooperatively navigate rule-constrained environments by adhering to mutually known navigational patterns, which may be represented as directional pathways or road lanes. Inferring these navigational patterns from incompletely observed environments is required for intelligent mobile robots operating in unmapped locations. However, algorithmically defining these navigational patterns is nontrivial. This paper presents the first self-supervised learning (SSL) method for learning to infer navigational patterns in real-world environments from partial observations only. We explain how geometric data augmentation, predictive world modeling, and an information-theoretic regularizer enables our model to predict an unbiased local directional soft lane probability (DSLP) field in the limit of infinite data. We demonstrate how to infer global navigational patterns by fitting a maximum likelihood graph to the DSLP field. Experiments show that our SSL model outperforms two SOTA supervised lane graph prediction models on the nuScenes dataset. We propose our SSL method as a scalable and interpretable continual learning paradigm for navigation by perception. Code is available at //github.com/robin-karlsson0/dslp.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.

In contrast to batch learning where all training data is available at once, continual learning represents a family of methods that accumulate knowledge and learn continuously with data available in sequential order. Similar to the human learning process with the ability of learning, fusing, and accumulating new knowledge coming at different time steps, continual learning is considered to have high practical significance. Hence, continual learning has been studied in various artificial intelligence tasks. In this paper, we present a comprehensive review of the recent progress of continual learning in computer vision. In particular, the works are grouped by their representative techniques, including regularization, knowledge distillation, memory, generative replay, parameter isolation, and a combination of the above techniques. For each category of these techniques, both its characteristics and applications in computer vision are presented. At the end of this overview, several subareas, where continuous knowledge accumulation is potentially helpful while continual learning has not been well studied, are discussed.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.