ترغب بنشر مسار تعليمي؟ اضغط هنا

Machine Learning for semi linear PDEs

55   0   0.0 ( 0 )
 نشر من قبل Xavier Warin
 تاريخ النشر 2018
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms.



قيم البحث

اقرأ أيضاً

We develop a physics-informed machine learning approach for large-scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two-dimensional steady-state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics-informed conditional Karhunen-Lo{e}ve expansion (PICKLE) method for modeling subsurface flow with unknown flux (Neumann) and varying head (Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large-scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen-Lo{e}ve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as $N_{FV}^{1.15}$) with the number of grid points $N_{FV}$, while that of MAP increases much faster as $N_{FV}^{3.28}$. We demonstrated that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).
Automated machine learning (AutoML) aims to find optimal machine learning solutions automatically given a machine learning problem. It could release the burden of data scientists from the multifarious manual tuning process and enable the access of do main experts to the off-the-shelf machine learning solutions without extensive experience. In this paper, we review the current developments of AutoML in terms of three categories, automated feature engineering (AutoFE), automated model and hyperparameter learning (AutoMHL), and automated deep learning (AutoDL). State-of-the-art techniques adopted in the three categories are presented, including Bayesian optimization, reinforcement learning, evolutionary algorithm, and gradient-based approaches. We summarize popular AutoML frameworks and conclude with current open challenges of AutoML.
Traditional differential privacy is independent of the data distribution. However, this is not well-matched with the modern machine learning context, where models are trained on specific data. As a result, achieving meaningful privacy guarantees in M L often excessively reduces accuracy. We propose Bayesian differential privacy (BDP), which takes into account the data distribution to provide more practical privacy guarantees. We also derive a general privacy accounting method under BDP, building upon the well-known moments accountant. Our experiments demonstrate that in-distribution samples in classic machine learning datasets, such as MNIST and CIFAR-10, enjoy significantly stronger privacy guarantees than postulated by DP, while models maintain high classification accuracy.
Machine learning algorithms designed to characterize, monitor, and intervene on human health (ML4H) are expected to perform safely and reliably when operating at scale, potentially outside strict human supervision. This requirement warrants a stricte r attention to issues of reproducibility than other fields of machine learning. In this work, we conduct a systematic evaluation of over 100 recently published ML4H research papers along several dimensions related to reproducibility. We find that the field of ML4H compares poorly to more established machine learning fields, particularly concerning data and code accessibility. Finally, drawing from success in other fields of science, we propose recommendations to data providers, academic publishers, and the ML4H research community in order to promote reproducible research moving forward.
In few-shot classification, we are interested in learning algorithms that train a classifier from only a handful of labeled examples. Recent progress in few-shot classification has featured meta-learning, in which a parameterized model for a learning algorithm is defined and trained on episodes representing different classification problems, each with a small labeled training set and its corresponding test set. In this work, we advance this few-shot classification paradigm towards a scenario where unlabeled examples are also available within each episode. We consider two situations: one where all unlabeled examples are assumed to belong to the same set of classes as the labeled examples of the episode, as well as the more challenging situation where examples from other distractor classes are also provided. To address this paradigm, we propose novel extensions of Prototypical Networks (Snell et al., 2017) that are augmented with the ability to use unlabeled examples when producing prototypes. These models are trained in an end-to-end way on episodes, to learn to leverage the unlabeled examples successfully. We evaluate these methods

الأسئلة المقترحة

التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا