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Detailed feedback on exercises helps learners become proficient but is time-consuming for educators and, thus, hardly scalable. This manuscript evaluates how well Generative Artificial Intelligence (AI) provides automated feedback on complex multimodal exercises requiring coding, statistics, and economic reasoning. Besides providing this technology through an easily accessible web application, this article evaluates the technology’s performance by comparing the quantitative feedback (i.e., points achieved) from Generative AI models with human expert feedback for 4,349 solutions to marketing analytics exercises. The results show that automated feedback produced by Generative AI (GPT-4) provides almost unbiased evaluations while correlating highly with (r = 0.94) and deviating only 6 % from human evaluations. GPT-4 performs best among seven Generative AI models, albeit at the highest cost. Comparing the models’ performance with costs shows that GPT-4, Mistral Large, Claude 3 Opus, and Gemini 1.0 Pro dominate three other Generative AI models (Claude 3 Sonnet, GPT-3.5, and Gemini 1.5 Pro). Expert assessment of the qualitative feedback (i.e., the AI’s textual response) indicates that it is mostly correct, sufficient, and appropriate for learners. A survey of marketing analytics learners shows that they highly recommend the app and its Generative AI feedback. An advantage of the app is its subject-agnosticism—it does not require any subject- or exercise-specific training. Thus, it is immediately usable for new exercises in marketing analytics and other subjects.
The human immune system is determined by the functionality of the human lymph node. With the use of high-throughput techniques in clinical diagnostics, a large number of data is currently collected. The new data on the spatiotemporal organization of cells offers new possibilities to build a mathematical model of the human lymph node - a virtual lymph node. The virtual lymph node can be applied to simulate drug responses and may be used in clinical diagnosis. Here, we review mathematical models of the human lymph node from the viewpoint of cellular processes. Starting with classical methods, such as systems of differential equations, we discuss the values of different levels of abstraction and methods in the range from artificial intelligence techniques formalism.
Highlights
• The Munich Procedure, developed for p-XRF data, standardises coefficient corrections.
• It ensures consistent, reproducible data, benefiting specialists in various industries.
• The protocol, documented as R-Skript, enhances accuracy and transparency of p-XRF data.
• Establishing a common baseline fosters discussion and improves the overall understanding of p-XRF.
Abstract
The Munich Procedure, a protocol presented as R code and initially developed on the basis of archaeometric portable X-ray fluorescence (p-XRF) data, offers adaptability and standardisation to evaluate coefficient corrections. These corrections are derived from linear regressions calculated by comparing p-XRF values with laboratory chemical analyses of the same sample set. The versatility of this procedure allows collaboration and ensures consistent data structure. Not tied to specific instrumentation, this approach helps to universally improve the accuracy of p-XRF data, benefiting specialists in a variety of industries. By providing a common baseline for performance evaluation, it enables discussion across different applications.
We introduce a novel technique that utilizes a physics-driven deep learning method to reconstruct the dense matter equation of state from neutron star observables, particularly the masses and radii. The proposed framework involves two neural networks: one to optimize the EoS using Automatic Differentiation in the unsupervised learning scheme; and a pre-trained network to solve the Tolman–Oppenheimer–Volkoff (TOV) equations. The gradient-based optimization process incorporates a Bayesian picture into the proposed framework. The reconstructed EoS is proven to be consistent with the results from conventional methods. Furthermore, the resulting tidal deformation is in agreement with the limits obtained from the gravitational wave event, GW170817.
PolarCAP – A deep learning approach for first motion polarity classification of earthquake waveforms
(2022)
Highlights
• We present PolarCAP, a deep learning model that can classify the polarity of a waveform with a 98% accuracy.
• The first-motion polarity of seismograms is a useful parameter, but its manual determination can be laborious and imprecise.
• We demonstrate that in several cases the model can assign trace polar-ity more accurately than a human analyst.
Abstract
The polarity of first P-wave arrivals plays a significant role in the effective determination of focal mechanisms specially for smaller earthquakes. Manual estimation of polarities is not only time-consuming but also prone to human errors. This warrants a need for an automated algorithm for first motion polarity determination. We present a deep learning model - PolarCAP that uses an autoencoder architecture to identify first-motion polarities of earth-quake waveforms. PolarCAP is trained in a supervised fashion using more than 130,000 labelled traces from the Italian seismic dataset (INSTANCE) and is cross-validated on 22,000 traces to choose the most optimal set of hyperparameters. We obtain an accuracy of 0.98 on a completely unseen test dataset of almost 33,000 traces. Furthermore, we check the model generalizability by testing it on the datasets provided by previous works and show that our model achieves a higher recall on both positive and negative polarities.
Structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, Molecular Dynamics (MD) simulations enable us to investigate these thermally activated processes with an atomic level of resolution. In practice, an exponentially large fraction of computational resources must be invested to simulate thermal fluctuations in metastable states. Path sampling methods focus the computational power on sampling the rare transitions between states. One of their outstanding limitations is to efficiently generate paths that visit significantly different regions of the conformational space. To overcome this issue, we introduce a new algorithm for MD simulations that integrates machine learning and quantum computing. First, using functional integral methods, we derive a rigorous low-resolution spatially coarse-grained representation of the system’s dynamics, based on a small set of molecular configurations explored with machine learning. Then, we use a quantum annealer to sample the transition paths of this low-resolution theory. We provide a proof-of-concept application by simulating a benchmark conformational transition with all-atom resolution on the D-Wave quantum computer. By exploiting the unique features of quantum annealing, we generate uncorrelated trajectories at every iteration, thus addressing one of the challenges of path sampling. Once larger quantum machines will be available, the interplay between quantum and classical resources may emerge as a new paradigm of high-performance scientific computing. In this work, we provide a platform to implement this integrated scheme in the field of molecular simulations.
Gradient-consistent enrichment of finite element spaces for the DNS of fluid-particle interaction
(2019)
Highlights
• Monolithic scheme for particulate flows preventing an oscillating pressure along the interface.
• The choice of enriching shape functions is driven by the properties of its gradient instead of its value.
• The choice of enriching shape functions inherits a natural stabilization on small cut elements.
Abstract
We present gradient-consistent enriched finite element spaces for the simulation of free particles in a fluid. This involves forces being exchanged between the particles and the fluid at the interface. In an earlier work [23] we derived a monolithic scheme which includes the interaction forces into the Navier-Stokes equations by means of a fictitious domain like strategy. Due to an inexact approximation of the interface oscillations of the pressure along the interface were observed. In multiphase flows oscillations and spurious velocities are a common issue. The surface force term yields a jump in the pressure and therefore the oscillations are usually resolved by extending the spaces on cut elements in order to resolve the discontinuity. For the construction of the enriched spaces proposed in this paper we exploit the Petrov-Galerkin formulation of the vertex-centered finite volume method (PG-FVM), as already investigated in [23]. From the perspective of the finite volume scheme we argue that wrong discrete normal directions at the interface are the origin of the oscillations. The new perspective of normal vectors suggests to look at gradients rather than values of the enriching shape functions. The crucial parameter of the enrichment functions therefore is the gradient of the shape functions and especially the one of the test space. The distinguishing feature of our construction therefore is an enrichment that is based on the choice of shape functions with consistent gradients. These derivations finally yield a fitted scheme for the immersed interface. We further propose a strategy ensuring a well-conditioned system independent of the location of the interface. The enriched spaces can be used within any existing finite element discretization for the Navier-Stokes equation. Our numerical tests were conducted using the PG-FVM. We demonstrate that the enriched spaces are able to eliminate the oscillations.
Rotational test spaces for a fully-implicit FVM and FEM for the DNS of fluid-particle interaction
(2019)
The paper presents a fully-implicit and stable finite element and finite volume scheme for the simulation of freely moving particles in a fluid. The developed method is based on the Petrov-Galerkin formulation of a vertex-centered finite volume method (PG-FVM) on unstructured grids. Appropriate extension of the ansatz and test spaces lead to a formulation comparable to a fictitious domain formulation. The purpose of this work is to introduce a new concept of numerical modeling reducing the mathematical overhead which many other methods require. It exploits the identification of the PG-FVM with a corresponding finite element bilinear form. The surface integrals of the finite volume scheme enable a natural incorporation of the interface forces purely based on the original bilinear operator for the fluid. As a result, there is no need to expand the system of equations to a saddle-point problem. Like for fictitious domain methods the extended scheme treats the particles as rigid parts of the fluid. The distinguishing feature compared to most existing fictitious domain methods is that there is no need for an additional Lagrange multiplier or other artificial external forces for the fluid-solid coupling. Consequently, only one single solve for the derived linear system for the fluid together with the particles is necessary and the proposed method does not require any fractional time stepping scheme to balance the interaction forces between fluid and particles. For the linear Stokes problem we will prove the stability of both schemes. Moreover, for the stationary case the conservation of mass and momentum is not violated by the extended scheme, i.e. conservativity is accomplished within the range of the underlying, unconstrained discretization scheme. The scheme is applicable for problems in two and three dimensions.
We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain Henry saltwater intrusion problem. Unknown porosity, permeability and recharge parameters are modelled by using random fields. The classical deterministic Henry problem is non-linear and time-dependent, and can easily take several hours of computing time. Uncertain settings require the solution of multiple realisations of the deterministic problem, and the total computational cost increases drastically. Instead of computing of hundreds random realisations, typically the mean value and the variance are computed. The standard methods such as the Monte Carlo or surrogate-based methods are a good choice, but they compute all stochastic realisations on the same, often, very fine mesh. They also do not balance the stochastic and discretisation errors. These facts motivated us to apply the MLMC method. We demonstrate that by solving the Henry problem on multi-level spatial and temporal meshes, the MLMC method reduces the overall computational and storage costs. To reduce the computing cost further, parallelization is performed in both physical and stochastic spaces. To solve each deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion.
Current deep learning methods are regarded as favorable if they empirically perform well on dedicated test sets. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving data is investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten. However, comparison of individual methods is nevertheless performed in isolation from the real world by monitoring accumulated benchmark test set performance. The closed world assumption remains predominant, i.e. models are evaluated on data that is guaranteed to originate from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown and corrupted instances. In this work we critically survey the literature and argue that notable lessons from open set recognition, identifying unknown examples outside of the observed set, and the adjacent field of active learning, querying data to maximize the expected performance gain, are frequently overlooked in the deep learning era. Hence, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Finally, the established synergies are supported empirically, showing joint improvement in alleviating catastrophic forgetting, querying data, selecting task orders, while exhibiting robust open world application.