Nonconforming tetrahedral mixed finite elements for elasticity

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method may be viewed as the three-dimensional analogue of a previously developed element in two dimensions. As in that case, a variant of the method is proposed as well, in which the displacement approximation is reduced to piecewise rigid motions and the stress space is reduced accordingly, but the linear convergence is retained.Comment: 13 pages, 2 figure

Mixed finite element methods for linear elasticity with weakly imposed symmetry

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger--Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.Comment: to appear in Mathematics of Computatio

Persuasive Technology for Learning and Teaching – The EuroPLOT Project

The concept of persuasive design has demonstrated its benefits by changing human behavior in certain situations, but in the area of education and learning, this approach has rarely been used. To change this and to study the feasibility of persuasive technology in teaching and learning, the EuroPLOT project (PLOT = Persuasive Learning Objects and Technologies) has been funded 2010-2013 by the Education, Audiovisual and Culture Executive Agency (EACEA) in the Life-long Learning (LLL) programme. In this program two tools have been developed (PLOTMaker and PLOTLearner) which allow to create learning objects with inherently persuasive concepts embedded. These tools and the learning objects have been evaluated in four case studies: language learning (Ancient Hebrew), museum learning (Kaj Munk Museum, Denmark), chemical handling, and academic Business Computing. These case studies cover a wide range of different learning styles and learning groups, and the results obtained through the evaluation of these case studies show the wide range of success of persuasive learning. They also indicate the limitations and areas where improvements are required

Demonstration of PLOTs from the EuroPLOT project

The EuroPLOT project (2010-2013) has been funded to explore the concept of persuasive design for learning and teaching. It has developed Persuasive Learn-ing Objects and Technologies (PLOTs), manifested in two tools and a set of learning objects that have been tested and evaluated in four different case studies. These PLOTs will be shown in this demonstration, and the participants can try them out and experience for themselves the impact of persuasive technology that is embedded in these PLOTs. This will be one authoring tool (PLOTMaker) and one delivery tool (PLOTLearner). Furthermore, there will be learning objects shown which have been developed for those four different case studies. All of these PLOTs have already been tested and evaluated during case studies with real learners

Impact of and solutions to effects of climate changes for Longyearbyen, Svalbard, Norway

Climate changes forces us to make significant mitigation and adaptation measures. As temperature rises and the environmental conditions changes, a variety of challenges occur. Across the whole globe, harming consequences are already being experienced. The Arctic region is particularly vulnerable to changes in Earth's climate system, especially because of the albedo effect, and the region is already heavily impacted. Primarily through the melting of ice, both sea ice and glaciers, permafrost thawing and changing precipitation patterns. Longyearbyen, Svalbard, is one examples of a society having to change as a direct result of global warming. This paper focuses on the challenges Longyearbyen will be facing and possible adaption methods and solutions. Because of environmental changes, the risk of natural hazards will increase, infrastructure will get damaged and traditional engineering methods will be impossible to implement. This is threatening to human lives as well as the habitat and survival of mammals, birds, and plants. It will be essential to find ways to predict and limit the effects of climate challenges, by protecting people and infrastructure from them. This will require innovation, adaption and risk-taking. By investigating the climate challenges facing Longyearbyen and possible ways to address them, this paper emphasizes the urgency of tackling the effects of climate changes in the Arctic in order to protect the communities in the Arctic region.publishedVersio

Persuasive Technology for Learning in Business Context

"Persuasive Design is a relatively new concept which employs general principles of persuasion that can be implemented in persuasive technology. This concept has been introduced by BJ Fogg in 1998, who since then has further extended it to use computers for changing attitudes and behaviour. Such principles can be applied very well in learning and teaching: in traditional human-led learning, teachers always have employed persuasion as one of the elements of teaching. Persuasive technology moves these principles into the digital domain, by focusing on technology that inherently stimulates learners to learn more quickly and effectively. This is very relevant for the area of Business Management in several aspects: Consumer Behavior, Communications, Human Resource, Marketing & Advertising, Organisational Behavior & Leadership. The persuasive principles identified by BJ Fogg are: reduction, tunnelling, tailoring, suggestion, self-monitoring, surveillance, conditioning, simulation, social signals. Also relevant is the concept of KAIROS, which means the just-in-time, at the right place provision of information/stimulus. In the EuroPLOT project (2010-2013) we have developed persuasive learning objects and tools (PLOTs) in which we have applied persuasive designs and principles. In this context, we have developed a pedagogical framework for active engagement, based on persuasive design in which the principles of persuasive learning have been formalised in a 6-step guide for persuasive learning. These principles have been embedded in two tools – PLOTmaker and PLOTLearner – which have been developed for creating persuasive learning objects. The tools provide specific capability for implementing persuasive principles at the very beginning of the design of learning objects. The feasibility of employing persuasive learning concepts with these tools has been investigated in four different case studies with groups of teachers and learners from realms with distinctly different teaching and learning practices: Business Computing, language learning, museum learning, and chemical substance handling. These case studies have involved the following learner target groups: school children, university students, tertiary students, vocational learners and adult learners. With regards to the learning context, they address archive-based learning, industrial training, and academic teaching. Alltogether, these case studies include participants from Sweden, Africa (Madagascar), Denmark, Czech Republic, and UK. One of the outcomes of this investigation was that one cannot apply a common set of persuasive designs that would be valid for general use in all situations: on the contrary, the persuasive principles are very specific to learning contexts and therefore must be specifically tailored for each situation. Two of these case studies have a direct relevance to education in the realm of Business Management: Business Computing and language learning (for International Business). In this paper we will present the first results from the evaluation of persuasive technology driven learning in these two relevant areas.

Finite element exterior calculus: from Hodge theory to numerical stability

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of partial differential equations that are related to differential complexes so that de Rham cohomology and Hodge theory are key tools for the continuous problem. After a brief introduction to finite element methods, the discretization methods we consider, we develop an abstract Hilbert space framework for analyzing stability and convergence. In this framework, the differential complex is represented by a complex of Hilbert spaces and stability is obtained by transferring Hodge theoretic structures from the continuous level to the discrete. We show stable discretization is achieved if the finite element spaces satisfy two hypotheses: they form a subcomplex and there exists a bounded cochain projection from the full complex to the subcomplex. Next, we consider the most canonical example of the abstract theory, in which the Hilbert complex is the de Rham complex of a domain in Euclidean space. We use the Koszul complex to construct two families of finite element differential forms, show that these can be arranged in subcomplexes of the de Rham complex in numerous ways, and for each construct a bounded cochain projection. The abstract theory therefore applies to give the stability and convergence of finite element approximations of the Hodge Laplacian. Other applications are considered as well, especially to the equations of elasticity. Background material is included to make the presentation self-contained for a variety of readers.Comment: 74 pages, 8 figures; reorganized introductory material, added additional example and references; final version accepted by Bulletin of the AMS, added references to codes and adjusted some diagrams. Bulletin of the American Mathematical Society, to appear 201

Coherent energy and force uncertainty in deep learning force fields

In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely used modeling approach involves predicting both a mean and variance for each energy value. However, this model is not differentiable under the usual white noise assumption, so energy uncertainty does not naturally translate to force uncertainty. In this work we propose a machine learning potential energy model in which energy and force aleatoric uncertainty are linked through a spatially correlated noise process. We demonstrate our approach on an equivariant messages passing neural network potential trained on energies and forces on two out-of-equilibrium molecular datasets. Furthermore, we also show how to obtain epistemic uncertainties in this setting based on a Bayesian interpretation of deep ensemble models.Comment: Presented at Advancing Molecular Machine Learning - Overcoming Limitations [ML4Molecules], ELLIS workshop, VIRTUAL, December 8, 2023, unofficial NeurIPS 2023 side-even

Graph Neural Network Interatomic Potential Ensembles with Calibrated Aleatoric and Epistemic Uncertainty on Energy and Forces

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials