arXiv subjects

Alejandro M. Aragón

Publications and source records attributed to Alejandro M. Aragón.

13 recordsLinked to original sources

arXiv2026

$\partial^2 ( \mathrm{TO} ) $: A Dual Topological Derivative-Based Enriched Topology Optimization for Fracture Mitigation in 3-D Brittle Solids

We propose a fracture-mitigation topology optimization framework for 3-D brittle solids. The topology is described by a level set function parameterized by radial basis functions, and the structural response is computed using an interface-enriched finite element formulation. Dual topological derivatives serve two purposes. First, they are used to nucleate holes within the solid during the optimization process. Second, they are used to evaluate energy release rates (ERRs) along the entire boundary, requiring only the stress field from a single enriched finite element analysis of the uncracked geometry. For this purpose, penny-shaped cracks are assumed to nucleate using the maximum hoop stress criterion, at the locations of enriched nodes introduced along the boundary for accurate finite element analysis. Because ERR estimates depend sensitively on stress accuracy, we compute a nodal stress field using a non-local stress-recovery procedure. The topology optimization objective aggregates the boundary ERRs using a $p$-mean function. Three-dimensional numerical examples, including the commonly studied L-bracket benchmark problem, demonstrate the capability of the proposed framework.

cs.CE↗

arXiv2026

A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of such systems can often be described by stochastic differential equations, a central challenge is understanding how noise influences the inference of system parameters and dynamics from data. Traditional symbolic regression methods can uncover governing equations but typically ignore uncertainty. Conversely, Gaussian processes provide principled uncertainty quantification but offer little insight into the underlying dynamics. In this work, we bridge this gap with a hybrid symbolic regression-probabilistic machine learning framework that recovers the symbolic form of the governing equations while simultaneously inferring uncertainty in the system parameters. The framework combines deep symbolic regression with Gaussian process-based maximum likelihood estimation to separately model the deterministic dynamics and the noise structure, without requiring prior assumptions about their functional forms. We verify the approach on numerical benchmarks, including harmonic, Duffing, and van der Pol oscillators, and validate it on an experimental system of coupled biological oscillators exhibiting synchronization, where the algorithm successfully identifies both the symbolic and stochastic components. The framework is data-efficient, requiring as few as 100-1000 data points, and robust to noise - demonstrating its broad potential in domains where uncertainty is intrinsic and both the structure and variability of dynamical systems must be understood.

cs.LG↗

arXiv2026

Cascade of Modal Interactions in Nanomechanical Resonators with Soft Clamping

We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.

cond-mat.mes-hall↗

arXiv2025

ARCADE: An interactive playground for real-time immersed topology optimization

Topology optimization (TO) has found applications across a wide range of disciplines but remains underutilized in practice. Key barriers to broader adoption include the absence of versatile commercial software, the need for specialized expertise, and high computational demands. Additionally, challenges such as ensuring manufacturability, optimizing hyper-parameters, and integrating subjective design elements like aesthetics further hinder its widespread use. Emerging technologies like augmented reality (AR) and virtual reality (VR) offer transformative potential for TO. By enabling intuitive, gesture-based human-computer interactions, these immersive tools bridge the gap between human intuition and computational processes. They provide the means to integrate subjective human judgment into optimization workflows in real time, creating a paradigm shift toward interactive and immersive design. Here we introduce the concept of immersive topology optimization (ITO) as a novel design paradigm that leverages AR environments for TO. To demonstrate this concept, we present ARCADE: Augmented Reality Computational Analysis and Design Environment. Developed in Swift for the Apple Vision Pro mixed reality headset, ARCADE enables users to define, manipulate, and solve structural optimization problems within an augmented reality setting. By incorporating real-time human interaction and visualization of the design in its intended target location, ARCADE has the potential to reduce lead times, enhance manufacturability, and improve design integration. Although initially developed for structural optimization, ARCADE's framework could be extended to other disciplines, paving the way for a new era of interactive and immersive computational design.

cs.CE↗

arXiv2024

Dissipation Dilution-Driven Topology Optimization for Maximizing the $Q$ Factor of Nanomechanical Resonators

The quality factor ($Q$ factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high $Q$ factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable $Q$ factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh -- i.e., without assuming any symmetries -- we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.

cond-mat.mes-hall↗

arXiv2023

Characterizing multi-mode nonlinear dynamics of nanomechanical resonators

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modelling methodology based on FEM simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven opto-thermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multi-stability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behaviour.

cond-mat.mes-hall↗

arXiv2022

A machine learning approach for fighting the curse of dimensionality in global optimization

Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality. Furthermore, multimodal cost functions render local gradient-based search techniques ineffective. To overcome these difficulties, we propose to trim uninteresting regions of the search space where global optima are unlikely to be found by means of autoencoders, exploiting the lower intrinsic dimensionality of certain cost functions; optima are then searched over lower-dimensional latent spaces. The methodology is tested on benchmark functions and on multiple variations of a structural topology optimization problem, where we show that we can estimate this intrinsic lower dimensionality and based thereon obtain the global optimum at best or superior results compared to established optimization procedures at worst.

cs.LG↗

arXiv2022

Sensitivity of viscoelastic characterization in multi-harmonic atomic force microscopy

Quantifying the nanomechanical properties of soft-matter using multi-frequency atomic force microscopy (AFM) is crucial for studying the performance of polymers, ultra-thin coatings, and biological systems. Such characterization processes often make use of cantilever's spectral components to discern nanomechanical properties within a multi-parameter optimization problem. This could inadvertently lead to an over-determined parameter estimation with no clear relation between the identified parameters and their influence on the experimental data. In this work, we explore the sensitivity of viscoelastic characterization in polymeric samples to the experimental observables of multi-frequency intermodulation AFM. By performing simulations and experiments we show that surface viscoelasticity has negligible effect on the experimental data and can lead to inconsistent and often non-physical identified parameters. Our analysis reveals that this lack of influence of the surface parameters relates to a vanishing gradient and non-convexity while minimizing the objective function. By removing the surface dependency from the model, we show that the characterization of bulk properties can be achieved with ease and without any ambiguity. Our work sheds light on the sensitivity issues that can be faced when optimizing for a large number of parameters and observables in AFM operation, and calls for the development of new viscoelastic models at the nanoscale and improved computational methodologies for nanoscale mapping of viscoelasticity using AFM.

cond-mat.soft↗

arXiv2021

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multiple-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. The method's ability to ensure continuity of the displacement field -- without locking -- in mesh coupling problems, and to transfer fairly accurate tractions at contact interfaces -- without the need for contact stabilization -- is demonstrated by means of several examples. In addition, we show that the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.

cs.CE↗

arXiv2021

Edible meta-atoms

Metamaterials are artificial structures with unusual and superior properties that come from their carefully designed building blocks -- also called meta-atoms. Metamaterials have permeated large swatches of science, including electromagnetics and mechanics. Although metamaterials hold the promise for realizing technological advances, their potential to enhance interactions between humans and materials has remained unexplored. Here, we devise meta-atoms with tailored fracture properties to control mouthfeel sensory experience. Using chocolate as a model material, we first use meta-atoms to control the fracture anisotropy and the number of cracks and demonstrate that these properties are captured in mouthfeel experience. We further use topology optimization to rationally design edible meta-atoms with maximally anisotropic fracture strength. Our work opens avenues for the use of meta-atoms and metamaterials to control fracture and to enhance human-matter interactions.

cond-mat.soft↗

arXiv2020

An Interface-enriched Generalized Finite Element Method for Levelset-based Topology Optimization

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a levelset function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as standard the finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based levelset topology optimization generates correct topologies for well-known compliance minimization problems.

cs.CE↗

arXiv2014

A C++11 implementation of arbitrary-rank tensors for high-performance computing

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.

cs.MS↗

arXiv2013

A measure for the impact of research

The last few years have seen the proliferation of measures that quantify the scientific output of researches. Yet, these measures focus on productivity, thus fostering the "publish or perish" paradigm. This article proposes a measure that aims at quantifying the impact of research de-emphasizing productivity, thus providing scientists an alternative, conceivably fairer, evaluation of their work. Emphasis is placed on the scientist rather than on quantities that can grow unbounded. The measure, defined initially for manuscripts, is then extended to researchers and institutions.

cs.DL↗