Laplace neural operator for complex geometries

Neural operators have emerged as a new area of machine learning for learning mappings between function spaces. Recently, an expressive and efficient architecture, Fourier neural operator (FNO) has been developed by directly parameterising the integral kernel in the Fourier domain, and achieved significant success in different parametric partial differential equations. However, the Fourier transform of FNO requires the regular domain with uniform grids, which means FNO is inherently inapplicable to complex geometric domains widely existing in real applications. The eigenfunctions of the Laplace operator can also provide the frequency basis in Euclidean space, and can even be extended to Riemannian manifolds. Therefore, this research proposes a Laplace Neural Operator (LNO) in which the kernel integral can be parameterised in the space of the Laplacian spectrum of the geometric domain. LNO breaks the grid limitation of FNO and can be applied to any complex geometries while maintaining the discretisation-invariant property. The proposed method is demonstrated on the Darcy flow problem with a complex 2d domain, and a composite part deformation prediction problem with a complex 3d geometry. The experimental results demonstrate superior performance in prediction accuracy, convergence and generalisability.Comment: 21 pages, 15 figure

A Novel N-Acetylglutamate Synthase Architecture Revealed by the Crystal Structure of the Bifunctional Enzyme from Maricaulis maris

Novel bifunctional N-acetylglutamate synthase/kinases (NAGS/K) that catalyze the first two steps of arginine biosynthesis and are homologous to vertebrate N-acetylglutamate synthase (NAGS), an essential cofactor-producing enzyme in the urea cycle, were identified in Maricaulis maris and several other bacteria. Arginine is an allosteric inhibitor of NAGS but not NAGK activity. The crystal structure of M. maris NAGS/K (mmNAGS/K) at 2.7 Å resolution indicates that it is a tetramer, in contrast to the hexameric structure of Neisseria gonorrhoeae NAGS. The quaternary structure of crystalline NAGS/K from Xanthomonas campestris (xcNAGS/K) is similar, and cross-linking experiments indicate that both mmNAGS/K and xcNAGS are tetramers in solution. Each subunit has an amino acid kinase (AAK) domain, which is likely responsible for N-acetylglutamate kinase (NAGK) activity and has a putative arginine binding site, and an N-acetyltransferase (NAT) domain that contains the putative NAGS active site. These structures and sequence comparisons suggest that the linker residue 291 may determine whether arginine acts as an allosteric inhibitor or activator in homologous enzymes in microorganisms and vertebrates. In addition, the angle of rotation between AAK and NAT domains varies among crystal forms and subunits within the tetramer. A rotation of 26° is sufficient to close the predicted AcCoA binding site, thus reducing enzymatic activity. Since mmNAGS/K has the highest degree of sequence homology to vertebrate NAGS of NAGS and NAGK enzymes whose structures have been determined, the mmNAGS/K structure was used to develop a structural model of human NAGS that is fully consistent with the functional effects of the 14 missense mutations that were identified in NAGS-deficient patients

Rehaussement et détection des attributs sismiques 3D par techniques avancées d'analyse d'images

Moments have been extensively used in pattern recognition and image processing. In this thesis, we focus our attention on the study of 3D orthogonal Gaussian-Hermite moments, 2D and 3D Gaussian-Hermite moment invariants, fast algorithm of coherency attribute, and applications of seismic interpretation using moments methodology.We conduct seismic horizon auto-tracking methods from Gaussian-Hermite moments and moment invariants. We introduce multi-scale moment invariants approach. The experimental results show that method of 3D Gaussian-Hermite moments performs better than the most popular methods.We also approach seismic facies analysis based on feature vectors from 3D Gaussian-Hermite moments, and Self-Organizing Maps method with data visualization techniques. The excellent result shows that the integrated environment gives the best performance in interpreting the correct cluster structure.Finally, we introduce the parallel processing and volume visualization. Taking advantage of new performances by multi-threading and multi-cores technologies into seismic interpretation, we efficiently compute the seismic attributes and track the horizon. We also discuss volume rendering algorithm based on Open-Scene-Graph engine which provides better insight into the structure of seismic data.Les Moments ont été largement utilisés dans la reconnaissance de formes et dans le traitement d'image. Dans cette thèse, nous concentrons notre attention sur les 3D moments orthogonaux de Gauss-Hermite, les moments invariants 2D et 3D de Gauss-Hermite, l'algorithme rapide de l'attribut de cohérence et les applications de l'interprétation sismique en utilisant la méthode des moments.Nous étudions les méthodes de suivi automatique d'horizon sismique à partir de moments de Gauss-Hermite en cas de 1D et de 3D. Nous introduisons une approche basée sur une étude multi-échelle des moments invariants. Les résultats expérimentaux montrent que la méthode des moments 3D de Gauss-Hermite est plus performante que les autres algorithmes populaires.Nous avons également abordé l'analyse des faciès sismiques basée sur les caractéristiques du vecteur à partir des moments 3D de Gauss -Hermite, et la méthode de Cartes Auto-organisatrices avec techniques de visualisation de données. L'excellent résultat de l'analyse des faciès montre que l'environnement intégré donne une meilleure performance dans l'interprétation de la structure des clusters.Enfin, nous introduisons le traitement parallèle et la visualisation de volume. En profitant des nouvelles performances par les technologies multi-threading et multi-cœurs dans le traitement et l'interprétation de données sismiques, nous calculons efficacement des attributs sismiques et nous suivons l'horizon. Nous discutons également l'algorithme de rendu de volume basé sur le moteur Open-Scene-Graph qui permet de mieux comprendre la structure de données sismiques

3D Seismic Attributes Enhancement and Detection by Advanced Technology of Image Analysis

Les Moments ont été largement utilisés dans la reconnaissance de formes et dans le traitement d'image. Dans cette thèse, nous concentrons notre attention sur les 3D moments orthogonaux de Gauss-Hermite, les moments invariants 2D et 3D de Gauss-Hermite, l'algorithme rapide de l'attribut de cohérence et les applications de l'interprétation sismique en utilisant la méthode des moments.Nous étudions les méthodes de suivi automatique d'horizon sismique à partir de moments de Gauss-Hermite en cas de 1D et de 3D. Nous introduisons une approche basée sur une étude multi-échelle des moments invariants. Les résultats expérimentaux montrent que la méthode des moments 3D de Gauss-Hermite est plus performante que les autres algorithmes populaires.Nous avons également abordé l'analyse des faciès sismiques basée sur les caractéristiques du vecteur à partir des moments 3D de Gauss -Hermite, et la méthode de Cartes Auto-organisatrices avec techniques de visualisation de données. L'excellent résultat de l'analyse des faciès montre que l'environnement intégré donne une meilleure performance dans l'interprétation de la structure des clusters.Enfin, nous introduisons le traitement parallèle et la visualisation de volume. En profitant des nouvelles performances par les technologies multi-threading et multi-cœurs dans le traitement et l'interprétation de données sismiques, nous calculons efficacement des attributs sismiques et nous suivons l'horizon. Nous discutons également l'algorithme de rendu de volume basé sur le moteur Open-Scene-Graph qui permet de mieux comprendre la structure de données sismiques.Moments have been extensively used in pattern recognition and image processing. In this thesis, we focus our attention on the study of 3D orthogonal Gaussian-Hermite moments, 2D and 3D Gaussian-Hermite moment invariants, fast algorithm of coherency attribute, and applications of seismic interpretation using moments methodology.We conduct seismic horizon auto-tracking methods from Gaussian-Hermite moments and moment invariants. We introduce multi-scale moment invariants approach. The experimental results show that method of 3D Gaussian-Hermite moments performs better than the most popular methods.We also approach seismic facies analysis based on feature vectors from 3D Gaussian-Hermite moments, and Self-Organizing Maps method with data visualization techniques. The excellent result shows that the integrated environment gives the best performance in interpreting the correct cluster structure.Finally, we introduce the parallel processing and volume visualization. Taking advantage of new performances by multi-threading and multi-cores technologies into seismic interpretation, we efficiently compute the seismic attributes and track the horizon. We also discuss volume rendering algorithm based on Open-Scene-Graph engine which provides better insight into the structure of seismic data

Active transfer learning for data-driven manufacturing process modelling

Manufacturing process modelling (MPM) aims to construct high-fidelity digital predictive models of the concerned properties of products, processes or manufacturing systems for the further optimisation and improvement of manufacturing activities. Data-driven modelling methods, including machine learning and deep learning, have drawn immense attention to MPM problems because of their powerful representative ability. However, the labelled data of concerning properties in the manufacturing process is often insufficient and sparse because of the expensive and time-consuming experiments or simulations. The scarcity of labelled data hinders the further development of data-driven models in MPM problems. This paper proposes an active transfer learning framework by integrating active generation of labelled data and the processing of relevant data to reduce the requirements of labelled data. Firstly, the initial active labelling module introduces the generation of a more representative and informative labelled dataset rather than a randomly generated one. Then, the transfer learning model can extract the general information from the relevant data to address the information scarcity for the target task. Besides, the iterative active labelling module can determine to query promising new labelled data according to the performance of the current model. The effectiveness of the proposed framework is verified in a tool wear prediction case. The experimental outcomes demonstrate that the three modules of the framework can reduce the labelled data requirements and enhance the performance of the data-drive model under limited labelled data

Rotation and translation invariants of Gaussian-Hermite moments

Geometric moment invariants are widely used in many fields of image analysis and pattern recognition since their first introduction by Hu in 1962. A few years ago, Flusser has proved how to find the indepen- dent and complete set of geometric moment invariants corresponding to a given order. On the other hand, the properties of orthogonal moments show that they can be recognized as useful tools for image representation and reconstruction. Therefore, derivation of invariants from orthogonal moments becomes an interesting subject and some results have been reported in literature. In this paper, we pro- pose to use a family of orthogonal moments, called Gaussian-Hermite moments and defined with Her- mite polynomials, for deriving their corresponding invariants. The rotation invariants of Gaussian- Hermite moments can be achieved algebraically according to a property of Hermite polynomials. This approach is definitely different from the conventional methods which derive orthogonal moment invari- ants either by image normalization or by an expression as a linear combination of the invariants of geo- metric moments. One significant conclusion drawn is that the rotation invariants of Gaussian-Hermite moments have the identical forms to those of geometric moments. This coincidence is also proved math- ematically in the appendix of the paper. Moreover, the translation invariants could be easily constructed by translating the coordinate origin to the image centroid. The invariants of Gaussian-Hermite moments both to rotation and to translation are accomplished by the combination of these two kinds of invariants. Their rotational and translational invariance is evaluated by a set of transformed gray-level images. The numeric stabilities of the proposed invariant descriptors are also discussed under both noise-free and noisy conditions. The computational complexity and time for implementing such invariants are analyzed as well. In addition to this, the better performance of the Gaussian-Hermite invariants is experimentally demonstrated by pattern matching in comparison with geometric moment invariants

Sampling via the aggregation value for data-driven manufacturing

International audienceAbstract Data-driven modelling has shown promising potential in many industrial applications, while the expensive and time-consuming labelling of experimental and simulation data restricts its further development. Preparing a more informative but smaller dataset to reduce labelling efforts has been a vital research problem. Although existing techniques can assess the value of individual data samples, how to represent the value of a sample set remains an open problem. In this research, the aggregation value is defined using a novel representation for the value of a sample set by modelling the invisible redundant information as the overlaps of neighbouring values. The sampling problem is hence converted to the maximisation of the submodular function over the aggregation value. The comprehensive analysis of several manufacturing datasets demonstrates that the proposed method can provide sample sets with superior and stable performance compared with state-of-the-art methods. The research outcome also indicates its appealing potential to reduce labelling efforts for more data-scarcity scenarios

Triazole-linked transition state analogs as selective inhibitors against V. cholerae sialidase.

Sialidases or neuraminidases are enzymes that catalyze the cleavage of terminal sialic acids from oligosaccharides and glycoconjugates. They play important roles in bacterial and viral infection and have been attractive targets for drug development. Structure-based drug design has led to potent inhibitors against neuraminidases of influenza A viruses that have been used successfully as approved therapeutics. However, selective and effective inhibitors against bacterial and human sialidases are still being actively pursued. Guided by crystal structural analysis, several derivatives of 2-deoxy-2,3-didehydro-N-acetylneuraminic acid (Neu5Ac2en or DANA) were designed and synthesized as triazole-linked transition state analogs. Inhibition studies revealed that glycopeptide analog E-(TriazoleNeu5Ac2en)-AKE and compound (TriazoleNeu5Ac2en)-A were selective inhibitors against Vibrio cholerae sialidase, while glycopeptide analog (TriazoleNeu5Ac2en)-AdE selectively inhibited Vibrio cholerae and A. ureafaciens sialidases