22,768 research outputs found
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
Climate projections continue to be marred by large uncertainties, which
originate in processes that need to be parameterized, such as clouds,
convection, and ecosystems. But rapid progress is now within reach. New
computational tools and methods from data assimilation and machine learning
make it possible to integrate global observations and local high-resolution
simulations in an Earth system model (ESM) that systematically learns from
both. Here we propose a blueprint for such an ESM. We outline how
parameterization schemes can learn from global observations and targeted
high-resolution simulations, for example, of clouds and convection, through
matching low-order statistics between ESMs, observations, and high-resolution
simulations. We illustrate learning algorithms for ESMs with a simple dynamical
system that shares characteristics of the climate system; and we discuss the
opportunities the proposed framework presents and the challenges that remain to
realize it.Comment: 32 pages, 3 figure
SimpleTrack:Adaptive Trajectory Compression with Deterministic Projection Matrix for Mobile Sensor Networks
Some mobile sensor network applications require the sensor nodes to transfer
their trajectories to a data sink. This paper proposes an adaptive trajectory
(lossy) compression algorithm based on compressive sensing. The algorithm has
two innovative elements. First, we propose a method to compute a deterministic
projection matrix from a learnt dictionary. Second, we propose a method for the
mobile nodes to adaptively predict the number of projections needed based on
the speed of the mobile nodes. Extensive evaluation of the proposed algorithm
using 6 datasets shows that our proposed algorithm can achieve sub-metre
accuracy. In addition, our method of computing projection matrices outperforms
two existing methods. Finally, comparison of our algorithm against a
state-of-the-art trajectory compression algorithm show that our algorithm can
reduce the error by 10-60 cm for the same compression ratio
- …