In this article, we propose CE-Prompt, an enhanced version of Prompt-Tuning designed to address issues such as the instability of random initialization and inefficiencies caused by long text in pre-trained large language models (LLMs). Inspired by the multi-head attention mechanism, CE-Prompt introduces the concept of composite embedding, which utilizes multiple randomly initialized embedding layers to generate more expressive prompt representations. To effectively integrate the information expressed by these composite embeddings, an additive fusion approach is employed, allowing each prompt vector to capture task-specific information more comprehensively, thereby improving the model’s task adaptability and inference efficiency. Experimental results show that CE-Prompt outperforms traditional Prompt-Tuning methods, with average improvements of 0.82% in Bilingual Evaluation Understudy (BLEU)-4 and 0.65% in ROUGE-L. Additionally, time complexity analysis indicates that CE-Prompt significantly reduces computational costs during inference. Compared to other methods, it achieves higher efficiency with the same training parameter budget, providing a more efficient solution for practical deployment.
Variational phase field fracture models are now widely used to simulate crack propagation in structures. A critical aspect of these simulations is the correct determination of the propagation threshold of pre-existing cracks, as it highly relies on how the initial cracks are implemented. While prior studies briefly discuss initial crack implementation techniques, we present here a systematic investigation. Various techniques to introduce initial cracks in phase field fracture simulations are tested, from the crack explicit meshing to the replacement by a fully damaged phase field, including different variants for the boundary conditions. Our focus here is on phase field models aiming to approximate, in the $\Gamma$-convergence limit, Griffith quasi-static propagation in the framework of Linear Elastic Fracture Mechanics. Therefore, a sharp crack model from classic linear elastic fracture mechanics based on Griffith criterion is the reference in this work. To assess the different techniques to introduce initial cracks, we rely on path-following methods to compute the sharp crack and the phase field smeared crack solutions. The underlying idea is that path-following ensures staying at equilibrium at each instant so that any difference between phase field and sharp crack models can be attributed to numerical artifacts. Thus, by comparing the results from both models, we can provide practical recommendations for reliably incorporating initial cracks in phase field fracture simulations. The comparison shows that an improper initial crack implementation often requires the smeared crack to transition to a one-element-wide phase band to adequately represent a displacement jump along a crack. This transition increases the energy required to propagate the crack, leading to a significant overshoot in the force-displacement response. The take-home message is that to predict the propagation threshold accurately and avoid artificial toughening; the crack must be initialized either setting the phase field to its damage state over a one-element-wide band or meshing the crack explicitly as a one-element-wide slit and imposing the fully cracked state on the crack surface.
Andrey Latyshev, Jérémy Bleyer, Corrado Maurini
et al.
Many problems in solid mechanics involve general and non-trivial constitutive models that are difficult to express in variational form. Consequently, it can be challenging to define these problems in automated finite element solvers, such as the FEniCS Project, that use domain-specific languages specifically designed for writing variational forms. In this article, we describe a methodology and software framework for FEniCSx / DOLFINx that enables the expression of constitutive models in nearly any general programming language. We demonstrate our approach on two solid mechanics problems; the first is a simple von Mises elastoplastic model with isotropic hardening implemented with Numba, and the second a Mohr-Coulomb elastoplastic model with apex smoothing implemented with JAX. In the latter case we show that by leveraging JAX's algorithmic automatic differentiation transformations we can avoid error-prone manual differentiation of the terms necessary to resolve the constitutive model. We show extensive numerical results, including Taylor remainder testing, that verify the correctness of our implementation. The software framework and fully documented examples are available as supplementary material under the LGPLv3 or later license.
Prin aceasta se va explica soluţionarea problemei ipotezei Riemann aşa cum a fost ea oficial descrisă1 de E. Bombieri, de la Institutul Matematic Clay şi furnizarea unei argumentaţii realiste pentru aceasta. Scopul este de a lămuri contextul teoretic matematic al problemei şi de a da un răspuns corect la problema ridicată de Riemann, din această nouă perspectivă. Până acum nu au fost decât încercări nereuşite de a demonstra corectitudinea ipotezei, dar s-au folosit aceleaşi premise pentru rezolvarea unei probleme ce are de fapt o altă interpretare. Rezultatul este una din consecinţele fireşti ale unui studiu interdisciplinar personal2 mai amplu ce include rolul matematicii în exprimarea formalizată a realităţii. S-a folosit o abordare teoretică ce lămureşte mai bine formalismul matematic implicat. Soluţionarea problemei, căci nu este o demonstraţie a ipotezei, are un impact major asupra conceptelor matematice elementare cu care se operează în prezent, prin definirea lor mai precisă. Totodată arată că ipoteza Riemann nu are implicaţii în studiul numerelor prime, ci al domeniilor subeuclidiene. Deasemeni este important impactul asupra înţelegerii fizicii în general şi asupra fizicii cuantice în special.
Inteligența, adesea considerată apogeul cunoașterii umane, este un construct care i-a fascinat pe savanți, oameni de știință și filozofi de secole. Originile inteligenței pot fi urmărite până la călătoria evolutivă a vieții însăși. În lumea naturală, inteligența nu se limitează la oameni, ci este un produs al strategiilor de adaptare și supraviețuire a diferitelor specii. Inteligența exercită implicații profunde asupra indivizilor, influențând rezultatele academice, succesul în carieră, interacțiunile sociale și bunăstarea generală.