Related papers: Weakly-supervised learning on Schrodinger equation
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…
This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…
We present a learning-based approach to relight a single image of Lambertian and low-frequency specular objects. Our method enables inserting objects from photographs into new scenes and relighting them under the new environment lighting,…
In this paper, we propose a method for training neural networks when we have a large set of data with weak labels and a small amount of data with true labels. In our proposed model, we train two neural networks: a target network, the…
We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…
In this paper we study the Cauchy problem for the Landau Hamiltonian wave equation, with time dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a `very…
This paper deals with the weak error estimates of the exponential Euler method for semi-linear stochastic partial differential equations (SPDEs). A weak error representation formula is first derived for the exponential integrator scheme in…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
We investigate the class of quadratic detectors (i.e., the statistic is a bilinear function of the data) for the detection of poorly modeled gravitational transients of short duration. We point out that all such detection methods are…
Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than…
This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as…
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the so-called harmonic approximation of the Schrodinger…
Semi-weakly supervised semantic segmentation (SWSSS) aims to train a model to identify objects in images based on a small number of images with pixel-level labels, and many more images with only image-level labels. Most existing SWSSS…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as a smoothed stored elastic energy function, a yield surface, and a plastic flow that are evolved based on a set…
Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to…
The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest.…
In this work, we used a semi-supervised learning method to train deep learning model that can segment the brain MRI images. The semi-supervised model uses less labeled data, and the performance is competitive with the supervised model with…
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…