2,104 research outputs found
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks
Physics-informed neural networks (PINNs) have emerged as new data-driven PDE
solvers for both forward and inverse problems. While promising, the expensive
computational costs to obtain solutions often restrict their broader
applicability. We demonstrate that the computations in automatic
differentiation (AD) can be significantly reduced by leveraging forward-mode AD
when training PINN. However, a naive application of forward-mode AD to
conventional PINNs results in higher computation, losing its practical benefit.
Therefore, we propose a network architecture, called separable PINN (SPINN),
which can facilitate forward-mode AD for more efficient computation. SPINN
operates on a per-axis basis instead of point-wise processing in conventional
PINNs, decreasing the number of network forward passes. Besides, while the
computation and memory costs of standard PINNs grow exponentially along with
the grid resolution, that of our model is remarkably less susceptible,
mitigating the curse of dimensionality. We demonstrate the effectiveness of our
model in various PDE systems by significantly reducing the training run-time
while achieving comparable accuracy. Project page:
https://jwcho5576.github.io/spinn/Comment: To appear in NeurIPS 2022 Workshop on The Symbiosis of Deep Learning
and Differential Equations (DLDE) - II, 12 pages, 5 figures, full paper:
arXiv:2306.1596
Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters
As the world's largest radio telescope, the Square Kilometer Array (SKA) will
provide radio interferometric data with unprecedented detail. Image
reconstruction algorithms for radio interferometry are challenged to scale well
with TeraByte image sizes never seen before. In this work, we investigate one
such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image
reconstruction For radio INterferometry). In particular, we focus on the
challenging task of automatically finding the optimal regularization parameter
values. In practice, finding the regularization parameters using classical grid
search is computationally intensive and nontrivial due to the lack of ground-
truth. We adopt a greedy strategy where, at each iteration, the optimal
parameters are found by minimizing the predicted Stein unbiased risk estimate
(PSURE). The proposed self-tuned version of MUFFIN involves parallel and
computationally efficient steps, and scales well with large- scale data.
Finally, numerical results on a 3D image are presented to showcase the
performance of the proposed approach
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
- âŠ