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Deep Learning (DL), in particular deep neural networks (DNN), by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties—such as stability, conservation, and positivity—and accuracy are required. DL methods in their original forms are not capable of respecting the underlying mathematical models or achieving desired accuracy even in big-data regimes. On the other hand, many data-driven science and engineering problems, such as inverse problems, typically have limited experimental or observational data, and DL would overfit the data in this case. Leveraging information encoded in the underlying mathematical models, we argue, not only compensates missing information in low data regimes but also provides opportunities to equip DL methods with the underlying physics, and hence promoting better generalization. This paper develops a model-constrained deep learning approach and its variant TNet—a Tikhonov neural network—that are capable of learning not only information hidden in the training data but also in the underlying mathematical models to solve inverse problems governed by partial differential equations in low data regimes. We provide the constructions and some theoretical results for the proposed approaches for both linear and nonlinear inverse problems. Since TNet is designed to learn inverse solution with Tikhonov regularization, it is interpretable: in fact it recovers Tikhonov solutions for linear cases while potentially approximating Tikhonov solutions in any desired accuracy for nonlinear inverse problems. We also prove that data randomization can enhance not only the smoothness of the networks but also their generalizations. Comprehensive numerical results confirm the theoretical findings and show that with even as little as 1 training data sample for 1D deconvolution, 5 for inverse 2D heat conductivity problem, 100 for inverse initial conditions for time-dependent 2D Burgers’ equation, and 50 for inverse initial conditions for 2D Navier-Stokes equations, TNet solutions can be as accurate as Tikhonov solutions while being several orders of magnitude faster. This is possible owing to the model-constrained term, replications, and randomization. 

Serverless (or Function-as-a-Service) compute model enables new applications with dynamic scaling. However, all current Serverless systems are best-effort, and as we prove this means they cannot guarantee hard real-time deadlines, rendering them unsuitable for such real-time applications. We analyze a proposed extension of the Serverless model that adds a guaranteed invocation rate to the serverless model called Real-time Serverless. This approach aims to meet real-time deadlines with dynamically allocated function invocations. We first prove that the Serverless model does not support real-time guarantees. Next, we analyze Real-time Serverless, showing it can guarantee application real-time deadlines for rate-monotonic real-time workloads. Further, we derive bounds on the required invocation rate to meet any set of workload runtimes and periods. Subsequently, we explore an application technique, pre-invocation, and show that it can reduce the required guaranteed invocation rate. We derive bounds for the feasible rate guarantee reduction, and corresponding overhead in wasted compute resources. Finally, we apply the theoretical results to improve the experience quality of a distributed virtual reality/ augmented reality application as well as simplify the application design and resource management. 

Incorporating inductive biases is a promising approach for tackling challenging robot learning domains with sample-efficient solutions. This paper identifies partially observable domains where symmetries can be a useful inductive bias for efficient learning. Specifically, by encoding the equivariance regarding specific group symmetries into the neural networks, our actor-critic reinforcement learning agents can reuse solutions in the past for related scenarios. Consequently, our equivariant agents outperform non-equivariant approaches significantly in terms of sample efficiency and final performance, demonstrated through experiments on a range of robotic tasks in simulation and real hardware. 

We demonstrate a single-component hydrophilic photocrosslinkable copolymer system that incorporates all critical functionalities into one chain. This design allows for the creation of uniform functional organic coatings on a variety of substrates. The copolymers were composed of a poly(ethylene oxide)-containing monomer, a monomer that can release a primary amine upon UV light, and a monomer with reactive epoxide or cyclic dithiocarbonate with a primary amine. These copolymers are easily incorporated into the solution-casting process using polar solvents. Furthermore, the resulting coating can be readily stabilized through UV light-induced crosslinking, providing an advantage for controlling the surface properties of various substrates. The photocrosslinking capability further enables us to photolithographically define stable polymer domains in a desirable region. The resulting copolymer coatings were chemically versatile in immobilizing complex molecules by (i) post-crosslinking functionalization with the reactive groups on the surface and (ii) the formation of a composite coating by mixing varying amounts of a protein of interest, i.e., fish skin gelatin, which can form a uniform dual crosslinked network. The number of functionalization sites in a thin film could be controlled by tuning the composition of the copolymers. In photocrosslinking and subsequent functionalizations, we assessed the reactivity of the epoxide and cyclic dithiocarbonate with the generated primary amine. Moreover, the orthogonality of the possible reactions of the presented reactive functionalities in the crosslinked thin films with complex molecules is assessed. The resulting copolymer coatings were further utilized to define a hydrophobic surface or an active surface for the adhesion of biological objects.

 

Stream Processing Engines (SPEs) traditionally de-ploy applications on a set of shared workers (e.g., threads, processes, or containers) requiring complex performance man-agement by SPEs and application developers. We explore a new approach that replaces workers with Rate-based Abstract Ma-chines (RBAMs). This allows SPEs to translate stream operations into FaaS invocations, and exploit guaranteed invocation rates to manage performance. This approach enables SPE applications to achieve transparent and predictable performance. We realize the approach in the Storm-RTS system. Exploring 36 stream processing scenarios over 5 different hardware config-urations, we demonstrate several key advantages. First, Storm-RTS provides stable application performance and can enable flexible reconfiguration across cloud resource configurations. Sec-ond, SPEs built on RBAM can be resource-efficient and scalable. Finally, Storm-RTS allows the stream-processing paradigm to be extended from the cloud to the edge, using its performance stability to hide edge heterogeneity and resource competition. An experiment with 4 cloud and edge sites over 300 cores shows how Storm-RTS can support flexible reconfiguration and simple high-level declarative policies that optimize resource cost or other criteria.