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We propose a set of techniques to efficiently importance sample the derivatives of a wide range of Bidirectional Reflectance Distribution Function (BRDF) models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts, which are real-valued and can have negative values. This leads to a new source of variance arising from their change in sign. Real-valued functions cannot be perfectly importance sampled by a positive-valued PDF, and the direct application of BRDF sampling leads to high variance. Previous attempts at antithetic sampling only addressed the derivative with the roughness parameter of isotropic microfacet BRDFs. Our work generalizes BRDF derivative sampling to anisotropic microfacet models, mixture BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs.

Our method first decomposes the real-valued differential BRDF into a sum of single-signed functions, eliminating variance from a change in sign. Next, we importance sample each of the resulting single-signed functions separately. The first decomposition, positivization, partitions the real-valued function based on its sign, and is effective at variance reduction when applicable. However, it requires analytic knowledge of the roots of the differential BRDF, and for it to be analytically integrable too. Our key insight is that the single-signed functions can have overlapping support, which significantly broadens the ways we can decompose a real-valued function. Our product and mixture decompositions exploit this property, and they allow us to support several BRDF derivatives that positivization could not handle. For a wide variety of BRDF derivatives, our method significantly reduces the variance (up to 58× in some cases) at equal computation cost and enables better recovery of spatially varying textures through gradient-descent-based inverse rendering.

 

Cyber-Physical Systems (CPS) integrate computational elements with physical processes via sensors and actuators. While CPS is expected to have human-level intelligence, traditional machine learning which is trained on specific and isolated datasets seems insufficient to meet such expectation. In recent years, Large Language Models (LLMs), like GPT-4, have experienced explosive growth and show significant improvement in reasoning and language comprehension capabilities which promotes LLM-enabled CPS. In this paper, we present a comprehensive review of these studies about LLM-enabled CPS. First, we overview LLM-enabled CPS and the roles that LLM plays in CPS. Second, we categorize existing works in terms of the application domain and discuss their key contributions. Third, we present commonly-used metrics and benchmarks for LLM-enabled CPS evaluation. Finally, we discuss future research opportunities and corresponding challenges of LLM-enabled CPS. 

Cyber-Physical Systems (CPS) are integrations of computation, networking, and physical processes. The autonomy and self-adaptation capabilities of CPS mark a significant evolution from traditional control systems. Machine learning significantly enhances the functionality and efficiency of Cyber-Physical Systems (CPS). Large Language Models (LLM), like GPT-4, can augment CPS’s functionality to a new level by providing advanced intelligence support. This fact makes the applications above potentially unsafe and thus untrustworthy if deployed to the real world. We propose a comprehensive and general assurance framework for LLM-enabled CPS. The framework consists of three modules: (i) the context grounding module assures the task context has been accurately grounded (ii) the temporal Logic requirements specification module forms the temporal requirements into logic specifications for prompting and further verification (iii) the formal verification module verifies the output of the LLM and provides feedback as a guideline for LLM. The three modules execute iteratively until the output of LLM is verified. Experiment results demonstrate that our assurance framework can assure the LLM-enabled CPS. 

In this paper, we consider a setting inspired by spatial crowdsourcing platforms, where both workers and tasks arrive at different times, and each worker-task assignment yields a given reward. The key challenge is to address the uncertainty in the stochastic arrivals from both workers and the tasks. In this work, we consider a ubiquitous scenario where the arrival patterns of worker “types” and task “types” are not erratic but can be predicted from historical data. Specifically, we consider a finite time horizon T and assume that in each time-step the arrival of a worker and a task can be seen as an independent sample from two (different) distributions. Our model, called "Online Task Assignment with Two-Sided Arrival" (OTA-TSA), is a significant generalization of the classical online task-assignment problem when all the tasks are statically available. For the general case of OTA-TSA, we present an optimal non-adaptive algorithm (NADAP), which achieves a competitive ratio (CR) of at least 0.295. For a special case of OTA-TSA when the reward depends only on the worker type, we present two adaptive algorithms, which achieve CRs of at least 0.343 and 0.355, respectively. On the hardness side, we show that (1) no non-adaptive can achieve a CR larger than that of NADAP, establishing the optimality of NADAP among all non-adaptive algorithms; and (2) no (adaptive) algorithm can achieve a CR better than 0.581 (unconditionally) or 0.423 (conditionally on the benchmark linear program), respectively. All aforementioned negative results apply to even unweighted OTA-TSA when every assignment yields a uniform reward. At the heart of our analysis is a new technical tool, called "two-stage birth-death process", which is a refined notion of the classical birth-death process. We believe it may be of independent interest. Finally, we perform extensive numerical experiments on a real-world ride-share dataset collected in Chicago and a synthetic dataset, and results demonstrate the effectiveness of our proposed algorithms in practice. 

Polymers play an integral role in various applications, from everyday use to advanced technologies. In the era of machine learning (ML), polymer informatics has become a vital field for efficiently designing and developing polymeric materials. However, the focus of polymer informatics has predominantly centered on single-component polymers, leaving the vast chemical space of polymer blends relatively unexplored. This study employs a high-throughput molecular dynamics (MD) simulation combined with active learning (AL) to uncover polymer blends with enhanced thermal conductivity (TC) compared to the constituent single-component polymers. Initially, the TC of about 600 amorphous single-component polymers and 200 amorphous polymer blends with varying blending ratios are determined through MD simulations. The optimal representation method for polymer blends is identified, which involves a weighted sum approach that extends existing polymer representation from single-component polymers to polymer blends. An AL framework, combining MD simulation and ML, is employed to explore the TC of approximately 550,000 unlabeled polymer blends. The AL framework proves highly effective in accelerating the discovery of high-performance polymer blends for thermal transport. Additionally, we delve into the relationship between TC, radius of gyration (R_g), and hydrogen bonding, highlighting the roles of inter- and intra-chain interactions in thermal transport in amorphous polymer blends. A significant positive association between TC andR_gimprovement and an indirect contribution from H-bond interaction to TC enhancement are revealed through a log-linear model and an odds ratio calculation, emphasizing the impact of increasingR_gand H-bond interactions on enhancing polymer blend TC.