Neural network analysis of neutron and X-ray reflectivity data: Incorporating prior knowledge for tackling the phase problem

• URL: http://arxiv.org/abs/2307.05364v1
• Date: Wed, 28 Jun 2023 11:15:53 GMT
• Title: Neural network analysis of neutron and X-ray reflectivity data: Incorporating prior knowledge for tackling the phase problem
• Authors: Valentin Munteanu, Vladimir Starostin, Alessandro Greco, Linus Pithan, Alexander Gerlach, Alexander Hinderhofer, Stefan Kowarik, Frank Schreiber
• Abstract summary: We present an approach that utilizes prior knowledge to regularize the training process over larger parameter spaces. We demonstrate the effectiveness of our method in various scenarios, including multilayer structures with box model parameterization. In contrast to previous methods, our approach scales favorably when increasing the complexity of the inverse problem.
• Score: 141.5628276096321
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Due to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This so-called phase problem poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this, we present an approach that utilizes prior knowledge to regularize the training process over larger parameter spaces. We demonstrate the effectiveness of our method in various scenarios, including multilayer structures with box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. By leveraging the input of prior knowledge, we can improve the training dynamics and address the underdetermined ("ill-posed") nature of the problem. In contrast to previous methods, our approach scales favorably when increasing the complexity of the inverse problem, working properly even for a 5-layer multilayer model and an N-layer periodic multilayer model with up to 17 open parameters.

Related papers

• SMILE: Zero-Shot Sparse Mixture of Low-Rank Experts Construction From Pre-Trained Foundation Models [85.67096251281191]
  We present an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction. SMILE allows for the upscaling of source models into an MoE model without extra data or further training. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning.
  arXiv  Detail & Related papers  (2024-08-19T17:32:15Z)
• Explaining the Machine Learning Solution of the Ising Model [0.0]
  This work shows how it can be accomplished for the ferromagnetic Ising model, the main target of several machine learning (ML) studies in statistical physics. By using a neural network (NN) without hidden layers (the simplest possible) and informed by the symmetry of the Hamiltonian, an explanation is provided for the strategy used in finding the supervised learning solution. These results pave the way to a physics-informed explainable generalized framework, enabling the extraction of physical laws and principles from the parameters of the models.
  arXiv  Detail & Related papers  (2024-02-18T20:47:33Z)
• An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem [12.676629870617337]
  Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters. Due to limitations in observation, limited shots or receivers, and random noise, conventional inversion methods are confronted with numerous challenges. We provide an unsupervised learning approach aimed at accurately reconstructing physical velocity parameters.
  arXiv  Detail & Related papers  (2023-11-08T08:39:33Z)
• Training Integrable Parameterizations of Deep Neural Networks in the Infinite-Width Limit [0.0]
  Large-width dynamics has emerged as a fruitful viewpoint and led to practical insights on real-world deep networks. For two-layer neural networks, it has been understood that the nature of the trained model radically changes depending on the scale of the initial random weights. We propose various methods to avoid this trivial behavior and analyze in detail the resulting dynamics.
  arXiv  Detail & Related papers  (2021-10-29T07:53:35Z)
• Dynamic Neural Diversification: Path to Computationally Sustainable Neural Networks [68.8204255655161]
  Small neural networks with a constrained number of trainable parameters, can be suitable resource-efficient candidates for many simple tasks. We explore the diversity of the neurons within the hidden layer during the learning process. We analyze how the diversity of the neurons affects predictions of the model.
  arXiv  Detail & Related papers  (2021-09-20T15:12:16Z)
• Hybrid neural network reduced order modelling for turbulent flows with geometric parameters [0.0]
  This paper introduces a new technique mixing up a classical Galerkin-projection approach together with a data-driven method to obtain a versatile and accurate algorithm for the resolution of geometrically parametrized incompressible turbulent Navier-Stokes problems. The effectiveness of this procedure is demonstrated on two different test cases: a classical academic back step problem and a shape deformation Ahmed body application.
  arXiv  Detail & Related papers  (2021-07-20T16:06:18Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Multi-Task Learning for Multi-Dimensional Regression: Application to Luminescence Sensing [0.0]
  A new approach to non-linear regression is to use neural networks, particularly feed-forward architectures with a sufficient number of hidden layers and an appropriate number of output neurons. We propose multi-task learning (MTL) architectures. These are characterized by multiple branches of task-specific layers, which have as input the output of a common set of layers. To demonstrate the power of this approach for multi-dimensional regression, the method is applied to luminescence sensing.
  arXiv  Detail & Related papers  (2020-07-27T21:23:51Z)
• Total Deep Variation: A Stable Regularizer for Inverse Problems [71.90933869570914]
  We introduce the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. We achieve state-of-the-art results for numerous imaging tasks.
  arXiv  Detail & Related papers  (2020-06-15T21:54:15Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.