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Causal probabilistic graph-based models have gained widespread utility, enabling the modeling of cause-and-effect relationships across diverse domains. With their rising adoption in new areas, such as automotive system safety and machine learning, the need for an integrated lifecycle framework akin to DevOps and MLOps has emerged. Currently, a process reference for organizations interested in employing causal engineering is missing. To address this gap and foster widespread industrial adoption, we propose CausalOps, a novel lifecycle framework for causal model development and application. By defining key entities, dependencies, and intermediate artifacts generated during causal engineering, we establish a consistent vocabulary and workflow model. This work contextualizes causal model usage across different stages and stakeholders, outlining a holistic view of creating and maintaining them. CausalOps' aim is to drive the adoption of causal methods in practical applications within interested organizations and the causality community.

Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds. Given any arbitrary two-dimensional kaleidoscopic orbifold, we provide an algorithm to construct a Euclidean, spherical, or hyperbolic polygon to match the orbifold. This polygon is then used to create a room for which the polygon serves as the floor and the ceiling. With our system that implements M\"obius transformations, the user can interactively edit the scene and see the reflections of the edited objects. To correctly visualize non-Euclidean orbifolds, we adapt the rendering algorithms to account for the geodesics in these spaces, which light rays follow. Our interactive orbifold design system allows the user to create arbitrary two-dimensional kaleidoscopic orbifolds. In addition, our mirror-based orbifold visualization approach has the potential of helping our users gain insight on the orbifold, including its orbifold notation as well as its universal cover, which can also be the spherical space and the hyperbolic space.

In volume rendering, transfer functions are used to classify structures of interest, and to assign optical properties such as color and opacity. They are commonly defined as 1D or 2D functions that map simple features to these optical properties. As the process of designing a transfer function is typically tedious and unintuitive, several approaches have been proposed for their interactive specification. In this paper, we present a novel method to define transfer functions for volume rendering by leveraging the feature extraction capabilities of self-supervised pre-trained vision transformers. To design a transfer function, users simply select the structures of interest in a slice viewer, and our method automatically selects similar structures based on the high-level features extracted by the neural network. Contrary to previous learning-based transfer function approaches, our method does not require training of models and allows for quick inference, enabling an interactive exploration of the volume data. Our approach reduces the amount of necessary annotations by interactively informing the user about the current classification, so they can focus on annotating the structures of interest that still require annotation. In practice, this allows users to design transfer functions within seconds, instead of minutes. We compare our method to existing learning-based approaches in terms of annotation and compute time, as well as with respect to segmentation accuracy. Our accompanying video showcases the interactivity and effectiveness of our method.

Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and point-cloud representations of the input shape and neural operators based on graph and Fourier architectures to learn the solution operator. The graph neural operator handles irregular grids and transforms them into and from regular latent grids on which Fourier neural operator can be efficiently applied. GINO is discretization-convergent, meaning the trained model can be applied to arbitrary discretization of the continuous domain and it converges to the continuum operator as the discretization is refined. To empirically validate the performance of our method on large-scale simulation, we generate the industry-standard aerodynamics dataset of 3D vehicle geometries with Reynolds numbers as high as five million. For this large-scale 3D fluid simulation, numerical methods are expensive to compute surface pressure. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points. The cost-accuracy experiments show a $26,000 \times$ speed-up compared to optimized GPU-based computational fluid dynamics (CFD) simulators on computing the drag coefficient. When tested on new combinations of geometries and boundary conditions (inlet velocities), GINO obtains a one-fourth reduction in error rate compared to deep neural network approaches.

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms, that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout.

Momentum space transformations for incommensurate 2D electronic structure calculations are fundamental for reducing computational cost and for representing the data in a more physically motivating format, as exemplified in the Bistritzer-MacDonald model. However, these transformations can be difficult to implement in more complex systems such as when mechanical relaxation patterns are present. In this work, we aim for two objectives. Firstly, we strive to simplify the understanding and implementation of this transformation by rigorously writing the transformations between the four relevant spaces, which we denote real space, configuration space, momentum space, and reciprocal space. This provides a straight-forward algorithm for writing the complex momentum space model from the original real space model. Secondly, we implement this for twisted bilayer graphene with mechanical relaxation affects included. We also analyze the convergence rates of the approximations, and show the tight-binding coupling range increases for smaller relative twists between layers, demonstrating that the 3-nearest neighbor coupling of the Bistritzer-MacDonald model is insufficient when mechanical relaxation is included for very small angles. We quantify this and verify with numerical simulation.

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.

We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.