36,518 research outputs found
Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients
In this article, we build on previous work to present an optimization
algorithm for nonlinearly constrained multi-objective optimization problems.
The algorithm combines a surrogate-assisted derivative-free trust-region
approach with the filter method known from single-objective optimization.
Instead of the true objective and constraint functions, so-called fully linear
models are employed, and we show how to deal with the gradient inexactness in
the composite step setting, adapted from single-objective optimization as well.
Under standard assumptions, we prove convergence of a subset of iterates to a
quasi-stationary point and if constraint qualifications hold, then the limit
point is also a KKT-point of the multi-objective problem
Quantum Mechanics Lecture Notes. Selected Chapters
These are extended lecture notes of the quantum mechanics course which I am
teaching in the Weizmann Institute of Science graduate physics program. They
cover the topics listed below. The first four chapter are posted here. Their
content is detailed on the next page. The other chapters are planned to be
added in the coming months.
1. Motion in External Electromagnetic Field. Gauge Fields in Quantum
Mechanics.
2. Quantum Mechanics of Electromagnetic Field
3. Photon-Matter Interactions
4. Quantization of the Schr\"odinger Field (The Second Quantization)
5. Open Systems. Density Matrix
6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation
7. Mean Field Approaches for Many Body Systems -- Fermions and Boson
Sensitivity analysis for ReaxFF reparameterization using the Hilbert-Schmidt independence criterion
We apply a global sensitivity method, the Hilbert-Schmidt independence
criterion (HSIC), to the reparameterization of a Zn/S/H ReaxFF force field to
identify the most appropriate parameters for reparameterization. Parameter
selection remains a challenge in this context as high dimensional optimizations
are prone to overfitting and take a long time, but selecting too few parameters
leads to poor quality force fields. We show that the HSIC correctly and quickly
identifies the most sensitive parameters, and that optimizations done using a
small number of sensitive parameters outperform those done using a higher
dimensional reasonable-user parameter selection. Optimizations using only
sensitive parameters: 1) converge faster, 2) have loss values comparable to
those found with the naive selection, 3) have similar accuracy in validation
tests, and 4) do not suffer from problems of overfitting. We demonstrate that
an HSIC global sensitivity is a cheap optimization pre-processing step that has
both qualitative and quantitative benefits which can substantially simplify and
speedup ReaxFF reparameterizations.Comment: author accepted manuscrip
Can you hear your location on a manifold?
We introduce a variation on Kac's question, "Can one hear the shape of a
drum?" Instead of trying to identify a compact manifold and its metric via its
Laplace--Beltrami spectrum, we ask if it is possible to uniquely identify a
point on the manifold, up to symmetry, from its pointwise counting function
where here and form an orthonormal
basis for . This problem has a physical interpretation. You are placed
at an arbitrary location in a familiar room with your eyes closed. Can you
identify your location in the room by clapping your hands once and listening to
the resulting echos and reverberations?
The main result of this paper provides an affirmative answer to this question
for a generic class of metrics. We also probe the problem with a variety of
simple examples, highlighting along the way helpful geometric invariants that
can be pulled out of the pointwise counting function .Comment: 26 pages, 1 figur
Thread-safe lattice Boltzmann for high-performance computing on GPUs
We present thread-safe, highly-optimized lattice Boltzmann implementations,
specifically aimed at exploiting the high memory bandwidth of GPU-based
architectures. At variance with standard approaches to LB coding, the proposed
strategy, based on the reconstruction of the post-collision distribution via
Hermite projection, enforces data locality and avoids the onset of memory
dependencies, which may arise during the propagation step, with no need to
resort to more complex streaming strategies. The thread-safe lattice Boltzmann
achieves peak performances, both in two and three dimensions and it allows to
sensibly reduce the allocated memory ( tens of GigaBytes for order billions
lattice nodes simulations) by retaining the algorithmic simplicity of standard
LB computing. Our findings open attractive prospects for high-performance
simulations of complex flows on GPU-based architectures
Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective
This paper introduces a comprehensive, multi-stage machine learning
methodology that effectively integrates information systems and artificial
intelligence to enhance decision-making processes within the domain of
operations research. The proposed framework adeptly addresses common
limitations of existing solutions, such as the neglect of data-driven
estimation for vital production parameters, exclusive generation of point
forecasts without considering model uncertainty, and lacking explanations
regarding the sources of such uncertainty. Our approach employs Quantile
Regression Forests for generating interval predictions, alongside both local
and global variants of SHapley Additive Explanations for the examined
predictive process monitoring problem. The practical applicability of the
proposed methodology is substantiated through a real-world production planning
case study, emphasizing the potential of prescriptive analytics in refining
decision-making procedures. This paper accentuates the imperative of addressing
these challenges to fully harness the extensive and rich data resources
accessible for well-informed decision-making
Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio
This paper reviews the most common situations where one or more regularity
conditions which underlie classical likelihood-based parametric inference fail.
We identify three main classes of problems: boundary problems, indeterminate
parameter problems -- which include non-identifiable parameters and singular
information matrices -- and change-point problems. The review focuses on the
large-sample properties of the likelihood ratio statistic. We emphasize
analytical solutions and acknowledge software implementations where available.
We furthermore give summary insight about the possible tools to derivate the
key results. Other approaches to hypothesis testing and connections to
estimation are listed in the annotated bibliography of the Supplementary
Material
Offline and Online Models for Learning Pairwise Relations in Data
Pairwise relations between data points are essential for numerous machine learning algorithms. Many representation learning methods consider pairwise relations to identify the latent features and patterns in the data. This thesis, investigates learning of pairwise relations from two different perspectives: offline learning and online learning.The first part of the thesis focuses on offline learning by starting with an investigation of the performance modeling of a synchronization method in concurrent programming using a Markov chain whose state transition matrix models pairwise relations between involved cores in a computer process.Then the thesis focuses on a particular pairwise distance measure, the minimax distance, and explores memory-efficient approaches to computing this distance by proposing a hierarchical representation of the data with a linear memory requirement with respect to the number of data points, from which the exact pairwise minimax distances can be derived in a memory-efficient manner. Then, a memory-efficient sampling method is proposed that follows the aforementioned hierarchical representation of the data and samples the data points in a way that the minimax distances between all data points are maximally preserved. Finally, the thesis proposes a practical non-parametric clustering of vehicle motion trajectories to annotate traffic scenarios based on transitive relations between trajectories in an embedded space.The second part of the thesis takes an online learning perspective, and starts by presenting an online learning method for identifying bottlenecks in a road network by extracting the minimax path, where bottlenecks are considered as road segments with the highest cost, e.g., in the sense of travel time. Inspired by real-world road networks, the thesis assumes a stochastic traffic environment in which the road-specific probability distribution of travel time is unknown. Therefore, it needs to learn the parameters of the probability distribution through observations by modeling the bottleneck identification task as a combinatorial semi-bandit problem. The proposed approach takes into account the prior knowledge and follows a Bayesian approach to update the parameters. Moreover, it develops a combinatorial variant of Thompson Sampling and derives an upper bound for the corresponding Bayesian regret. Furthermore, the thesis proposes an approximate algorithm to address the respective computational intractability issue.Finally, the thesis considers contextual information of road network segments by extending the proposed model to a contextual combinatorial semi-bandit framework and investigates and develops various algorithms for this contextual combinatorial setting
Identifying Student Profiles Within Online Judge Systems Using Explainable Artificial Intelligence
Online Judge (OJ) systems are typically considered within programming-related courses as they yield fast and objective assessments of the code developed by the students. Such an evaluation generally provides a single decision based on a rubric, most commonly whether the submission successfully accomplished the assignment. Nevertheless, since in an educational context such information may be deemed insufficient, it would be beneficial for both the student and the instructor to receive additional feedback about the overall development of the task. This work aims to tackle this limitation by considering the further exploitation of the information gathered by the OJ and automatically inferring feedback for both the student and the instructor. More precisely, we consider the use of learning-based schemes—particularly, Multi-Instance Learning and classical Machine Learning formulations—to model student behaviour. Besides, Explainable Artificial Intelligence is contemplated to provide human-understandable feedback. The proposal has been evaluated considering a case of study comprising 2,500 submissions from roughly 90 different students from a programming-related course in a Computer Science degree. The results obtained validate the proposal: the model is capable of significantly predicting the user outcome (either passing or failing the assignment) solely based on the behavioural pattern inferred by the submissions provided to the OJ. Moreover, the proposal is able to identify prone-to-fail student groups and profiles as well as other relevant information, which eventually serves as feedback to both the student and the instructor.This work has been partially funded by the “Programa Redes-I3CE de investigacion en docencia universitaria del Instituto de Ciencias de la Educacion (REDES-I3CE-2020-5069)” of the University of Alicante. The third author is supported by grant APOSTD/2020/256 from “Programa I+D+I de la Generalitat Valenciana”
- …