Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically address the imposition of Dirichlet/Neumann boundary conditions over irregular domain boundaries. In this paper, we present a framework to neurally solve partial differential equations over domains with irregularly shaped (non-rectilinear) geometric boundaries. Our network takes in the shape of the domain as an input (represented using an unstructured point cloud, or any other parametric representation such as Non-Uniform Rational B-Splines) and is able to generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a novel approach for identifying the interior and exterior of the computational grid in a differentiable manner. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase a wide variety of applications, along with favorable comparisons with ground truth solutions.
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Large pretrained language models generate fluent text but are notoriously hard to controllably sample from. In this work, we study constrained sampling from such language models: generating text that satisfies user-defined constraints, while maintaining fluency and the model's performance in a downstream task. We propose MuCoLa -- a sampling procedure that combines the log-likelihood of the language model with arbitrary (differentiable) constraints in a single energy function, and then generates samples in a non-autoregressive manner. Specifically, it initializes the entire output sequence with noise and follows a Markov chain defined by Langevin Dynamics using the gradients of the energy function. We evaluate MuCoLa on text generation with soft and hard constraints as well as their combinations obtaining significant improvements over competitive baselines for toxicity avoidance, sentiment control, and keyword-guided generation.
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2021-12-09
在RL的许多实际应用中，观察来自环境的状态过渡是昂贵的。例如，在核聚变的等离子体控制问题中，计算给定的状态对对的下一个状态需要查询昂贵的过渡功能，这可以导致许多小时的计算机模拟或美元科学研究。这种昂贵的数据收集禁止应用标准RL算法，该算法通常需要大量观察来学习。在这项工作中，我们解决了有效地学习策略的问题，同时为转换函数进行最小数量的状态动作查询。特别是，我们利用贝叶斯最优实验设计的想法，以指导选择国家行动查询以获得高效学习。我们提出了一种采集功能，该函数量化了状态动作对将提供多少信息对Markov决策过程提供的最佳解决方案。在每次迭代时，我们的算法最大限度地提高了该采集功能，选择要查询的最具信息性的状态动作对，从而产生数据有效的RL方法。我们试验各种模拟的连续控制问题，并显示我们的方法学习最佳政策，最高$ 5 $ - $ 1,000 \倍的数据，而不是基于模型的RL基线，10 ^ 3美元 - $ 10 ^ 5 \ times比无模型RL基线更少的数据。我们还提供了几种消融比较，这指出了从获得数据的原理方法产生的大量改进。
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Levenberg-Marquardt（LM）优化算法已广泛用于解决机器学习问题。文学评论表明，当网络中的权重数不超过几百个时，LM对中等函数近似问题的LM非常强大而有效。相比之下，在处理模式识别或分类问题时，LM似乎并不表现，并且当网络变大时效率低（例如，超过500重量）。在本文中，我们利用一些现实世界飞机数据集利用LM算法的真正力量。在这些数据集上，大多数其他常用的优化器无法检测到飞机发动机的变化条件引起的异常。数据集的具有挑战性是时间序列数据的突然变化。我们发现LM优化器具有更好的近似突然变化的能力，并检测除其他优化器的异常。我们比较LM和几个其他优化器的这种异常/更改检测问题的性能。我们基于一系列措施评估了相对性能，包括网络复杂性（即权重的数量），拟合精度，拟合，培训时间，GPU和内存要求等的使用等措施。我们还讨论了Matlab中强大的LM实现问题Tensorflow用于推广LM算法的更多流行使用以及LM优化器的潜在使用进行大规模问题。
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