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Exterior-point optimization for sparse and low-rank optimization
Get PDFMany problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver (NExOS)—a first-order algorithm tailored to sparse and low-rank optimization problems. We consider the problem of minimizing a convex function over a nonconvex constraint set, where the set can be decomposed as the intersection of a compact convex set and a nonconvex set involving sparse or low-rank constraints. Unlike the convex relaxation approaches, NExOS finds a locally optimal point of the original problem by solving a sequence of penalized problems with strictly decreasing penalty parameters by exploiting the nonconvex geometry. NExOS solves each penalized problem by applying a first-order algorithm, which converges linearly to a local minimum of the corresponding penalized formulation under regularity conditions. Furthermore, the local minima of the penalized problems converge to a local minimum of the original problem as the penalty parameter goes to zero. We then implement and test NExOS on many instances from a wide variety of sparse and low-rank optimization problems, empirically demonstrating that our algorithm outperforms specialized methods
A new temperature evolution equation that enforces thermodynamic vapour–liquid equilibrium in multiphase flows - application to CO2 modelling
Get PDFThis work presents a novel framework for numerically simulating the depressurization of tanks and pipelines
containing carbon dioxide (CO2 ). The framework focuses on efficient solution strategies for the coupled system
of fluid flow equations and thermodynamic constraints. A key contribution lies in proposing a new set of
equations for phase equilibrium calculations which simplifies the traditional vapour–liquid equilibrium (VLE)
calculations for two-phase CO2 mixtures. The first major novelty resides in the reduction of the conventional
four-equation VLE system to a single equation, enabling efficient solution using a non-linear solver. This
significantly reduces computational cost compared to traditional methods. Furthermore, a second novelty is
introduced by deriving an ordinary differential equation (ODE) directly from the UV-Flash equation. This ODE
can be integrated alongside the governing fluid flow equations, offering a computationally efficient approach
for simulating depressurization processes
Entropy-stable model reduction of one-dimensional hyperbolic systems using rational quadratic manifolds
Get PDFIn this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems of nonlinear hyperbolic conservation laws. The so-called entropy stability property endows the semi-discrete ROMs with physically admissible behaviour. The method generalizes earlier results on entropy-stable ROMs constructed on linear spaces. The ROM works by evaluating the projected system on a well-chosen approximation of the state that ensures entropy stability. To ensure accuracy of the ROM after this approximation we locally enrich the tangent space of the reduced manifold with important quantities. Using numerical experiments on some well-known equations (the inviscid Burgers equation, shallow water equations and compressible Euler equations) we show the improved structure-preserving properties of our ROM compared to standard approaches and that our approximations have minimal impact on the accuracy of the ROM. We additionally generalize the recently proposed polynomial reduced manifolds to rational polynomial manifolds and show that this leads to an increase in accuracy for our experiments
Efficient learning of quantum states prepared with few fermionic non-Gaussian gates
Get PDFThe experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on n fermion modes prepared by any number of Gaussian and at most t non-Gaussian gates. By Jordan-Wigner mapping, this also includes n-qubit states prepared by nearest-neighbor matchgate circuits with at most t swap gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is poly(n,2t); thus if t=O(log(n)), it is efficient. We also show that, if t scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property-testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit-compilation method
Statistical and machine learning contributions to spatial and spatio-temporal point process modelling, with an application to Dutch fire risk prediction
Get PDFPoint pattern data are ubiquitous in both the natural environment and human activities. Spatial and spatio-temporal point processes are widely utilized to model the occurrence of random events across space and time. These models aim to uncover the underlying patterns of such events by analyzing environmental variables that influence their probabilities, and by testing, estimating and simulating spatial or spatio-temporal correlations. Despite significant advances in point process theory and methodology in the last decades, classical approaches still require continuous refinement and extension. This need arises from the distinctive characteristics of point pattern data in practical applications, as well as the increasing amount and complexity of data available in contemporary research. This thesis explores spatial and spatio-temporal modelling in the context of fire risk prediction in the Netherlands. Fire occurrences exhibit unique features that pose specific challenges in point process modelling. Four critical research questions are identified based on real applications of point process methods to the data. To address these challenges, we developed novel statistical and machine learning approaches, proposing targeted solutions that advance the state-of-the-art in the research domain
Footprint logic for object-oriented components (extended paper)
Get PDFWe introduce a new way of reasoning about invariance in terms of footprints in a program logic for object-oriented components. A footprint of an object-oriented component is formalized as a monadic predicate that describes which objects on the heap can be affected by the execution of the component. Assuming encapsulation, this amounts to specifying which objects of the component can be called. Adaptation of local specifications into global specifications amounts to showing invariance of assertions, which is ensured by means of a form of bounded quantification which excludes references to a given footprint. The new approach is compared to two existing approaches to reason about invariance: separation logic and dynamic frames
LogiCraft: A game modification framework for learning propositional logic
Get PDFLogic and formal reasoning are essential skills for programming and
computer science. Still, they are challenging to teach due to their
abstract nature. This paper explores how Game-Based Learning
(GBL) can simplify logic concepts, making them interactive and en-
gaging for young learners. We introduce LogiCraft, an educational
framework for co-designing board games that teach propositional
logic. The framework includes three illustrative tile-based board
games:¬SCR∧BL, Tautoblocks, and Deducto. These games teach
propositional logic by merging computational thinking with hands-
on gameplay. By integrating syntax and semantics in new ways,
¬SCR∧BL focuses on logic formulas construction and truth ta-
bles visualization, Tautoblocks introduces more advanced concepts
of negation, tautology, and contradiction, and Deducto highlights
translation and model-based reasoning. Playtesting sessions with
students and teachers suggest that our games can enhance logic
skills and promote cooperative learning. Our initial classroom re-
sults show potential for broader applications in game-based learn-
ing
Quantitative phase imaging with a multimode fiber
Get PDFLabel-free quantitative phase imaging is vital for optical microscopy and metrology applications. A multimode fiber stands out as a desirable platform for imaging. Here, we propose and experimentally demonstrate a non-interferometric non-iterative approach for high-speed high-resolution label-free quantitative phase imaging via a random light scattering in a multimode fiber
Christensen-Sinclair factorization via semidefinite programming
Get PDFWe show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also provides an efficient algorithm to compute the Christensen-Sinclair factorization