Integration Step Research Articles

Simulating the propagation of boundary-layer disturbances by solving boundary-value and initial-value problems

Abstract The article deals with the downstream propagation of small–amplitude disturbances of viscous incompressible laminar boundary layers, using the linearized equations for disturbance amplitudes. Two different methods are proposed. The first one solves a two-dimensional boundary-value problem, using a buffer-domain technique to mimic the outflow boundary condition. The second one solves a streamwise initial-value problem, using a spectral parabolization at each integration step. Both methods show good performance in simulating the propagation of the Tollmien–Schlichting waves and the Görtler vortices and can be applied to compute the spatial optimal disturbances.

Failing Forward in European Economic Governance: The Cyclicality of European Integration and Institutional Competition in the COVID‐19 Crisis

AbstractThe European Union's (EU's) response to the pandemic has been accompanied by reconfigurations in its institutional hierarchy, affecting the sites where institutional reforms are prepared and implemented. Whereas the Eurogroup drove reform during the euro crisis, the Commission had a more pronounced role in the development and implementation of pandemic instruments. This article ties in with failing‐forward arguments that view European integration as cyclical, arguing that this cyclicality also concerns the institutional dynamics in European economic governance. Based on expert interviews, official documents and reports, the analysis reconstructs and compares the institutional configurations during the euro crisis and the pandemic. Its findings suggest three modifications to ‘failing forward’: first, incomplete intergovernmental decisions are often the result of dominant particular interests rather than ‘lowest common denominator’ solutions; second, supranational bodies can exploit the delegitimization of intergovernmental solutions; and third, ad hoc measures can prolong the failing‐forward cycle and displace lasting integration steps.

Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters.

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest is only considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.

Elucidating the Molecular Determinants of the Binding Modes of a Third-Generation HIV-1 Integrase Strand Transfer Inhibitor: The Importance of Side Chain and Solvent Reorganization.

The first- and second-generation clinically used HIV-1 integrase (IN) strand transfer inhibitors (INSTIs) are key components of antiretroviral therapy (ART), which work by blocking the integration step in the HIV-1 replication cycle that is catalyzed by a nucleoprotein assembly called an intasome. However, resistance to even the latest clinically used INSTIs is beginning to emerge. Developmental third-generation INSTIs, based on naphthyridine scaffolds, are promising candidates to combat drug-resistant viral variants. Among these novel INSTIs, compound 4f exhibits two distinct conformations when binding with intasomes from HIV-1 and the closely related prototype foamy virus (PFV) despite the high structural similarity of their INSTI binding pockets. The molecular mechanism and the key active site residues responsible for these differing binding modes in closely related intasomes remain elusive. To unravel the molecular determinants governing the two distinct binding modes, we applied a novel molecular dynamics-based free energy method that utilizes alchemical pathways to overcome the sampling challenges associated with transitioning between the two bound conformations of ligand 4f within the crowded environments of the INSTI binding pockets in these intasomes. The calculated conformational free energies successfully recapitulate the experimentally observed binding mode preferences in the two viral intasomes. Analysis of the simulated structures suggests that the observed binding mode preferences are caused by amino acid residue differences in both the front and the central catalytic sub-pocket of the INSTI binding site in HIV-1 and PFV. Additional free energy calculations on mutants of HIV-1 and PFV revealed that while both sub-pockets contribute to binding mode selection, the central sub-pocket plays a more important role. These results highlight the importance of both side chain and solvent reorganization, as well as the conformational entropy in determining the ligand binding mode, and will help inform the development of more effective INSTIs for combatting drug-resistant viral variants.

To the algorithmization of the task of optimizing the transportation work of locomotives

A classification of optimization problems for the transportation work of locomotives and various possible methods of a numerical method for solving differential equations of the form y′=f(x,y) by the chord method are given. A verbal-operator format for the algorithm for solving the specified differential equations is proposed, taking into account the implementation of additional graphical constructions in the current integration interval for the average speed of the train. The algorithm for choosing a preliminary step of integration over the independent variable “path” is substantiated, the found value of which, according to the method of integrating a differential equation of the form y′=f(x,y) proposed for the author of this article, is used in subsequent calculations, including, which is very important, on the variable step of integration. It is recommended, based on the algorithms proposed by the author, to develop programs for traction and energy (economic) calculations for locomotives of electric traction and high-speed passenger trains.

Расчетно-экспериментальное исследование закрученного кольцевого потока

In the course of work on the energy perfection of thermal control systems for spacecraft with a twophase circuit, the issue of partial regeneration of thermal energy into electrical energy in a low-speed turbogenerator is considered, part of the design work requires computational modeling during the transport of swirling flows in the axial direction from the external input to the input plane into the impeller, which determines the need for theoretical and experimental elaboration of the problem. The paper considers transformations of equations for changing the amount of fluid motion in boundary conditions of an axial annular channel with fixed cylindrical surfaces. Assuming the symmetry axis of the flows using the integral form of writing the continuity equation, the relations are obtained in the form of two differential equations with expressed derivatives along the channel axis for the total pressure p* and the circumferential velocity constant Cu = UR (const — at the integration step). The equation forms the basis of the algorithm of integration in finite differences supplemented by a system of service equations describing the friction stress, thermodynamic parameters, etc. Test calculations are carried out using real parameters, the results are analyzed.

Predictive Temperature Control of an Industrial Heating Process

This paper presents an approach to control the temperature of an industrial heating process where a workpiece is transported through a heating unit in order to reach a certain temperature. To control this process is challenging due to the variable and possibly abruptly changing feed rate while requiring the final workpiece temperature to be maintained at a constant value. The speed itself cannot be influenced by the control system. However, its future trajectory is known to a certain extent at runtime. A model predictive controller is presented, which is characterized by the fact that the prediction horizon is dynamically adjusted to the transportation speed, that the traveled distance of the workpiece within the horizon is constant. Moreover, the step size of the integrator is also adapted, yielding a constant number of integration steps despite large variations in velocity. Because of the special structure of the used model, the system state cannot be reused from one time step to the next and needs to be reconstructed in a receeding horizon fashion, even if the model was perfect. This is also a distinctive feature of the presented control scheme. Simulation and measurement results are provided, showing that the presented controller achieves promising results and outperforms the existing lookup-table-based controller currently in use.

FESD-J: Finite Elements with Switch Detection for numerical optimal control of rigid bodies with impacts and Coulomb friction

The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method (Nurkanović et al., 2022) to the dynamic equations of multiple rigid bodies that exhibit state jumps due to impacts and Coulomb friction. This new method is referred to as FESD with Jumps (FESD-J). Starting from the standard Runge–Kutta equations, we let the integration step sizes be degrees of freedom. Additional constraints are introduced to ensure exact switch detection and to remove spurious degrees of freedom if no switches occur. Moreover, at the boundaries of each integration interval (finite element), we impose the impact equations in their complementarity form, at both the position and velocity level. They compute the normal and tangential impulses in case of contact making. Otherwise, they are reduced to the continuity conditions for the velocities. FESD-J treats multiple contacts, where each contact can have a different coefficient of restitution and friction. All methods introduced in this paper are implemented in the open-source software package NOSNOC (Nurkanović and Diehl, 2022). We illustrate the use of FESD-J in both simulation and optimal control examples.

Kinematically excited beam vibrations under random perturbations

There is numerous information in the technical and scientific literature that often the sources of forced kinematically excited oscillations have a clearly expressed random nature. Kinematically excited vibrations of beams are considered. Their sources are random disturbances. Steady (in a probabilistic sense) vibrations of beams are studied. As a consequence, the transverse vibrations of the beam will also be random, and it becomes necessary and expedient to switch to stochastic motion models.
 Introduction. For a random perturbation process, a spectral matrix is specified. Initial conditions for the equations are not required. The boundary conditions are similar to those used for free and kinematically excited deterministic oscillations. The task is to find the spectral matrix of the random field of beam deviations and dispersion for a given spectral matrix. The question of determining the mathematical expectation is not raised. It is argued that it can be easily reduced to known deterministic problems.
 Methods. To carry out specific calculations, a model of kinematic disturbances is used in the form of a vector N-dimensional stationary random process with stationary connected components that have hidden periodicities (characteristic frequencies). A test example was completed to determine the dispersion and standard deviation of displacements. The numerical integration step was adopted after numerical experiments. When performing calculations, the parity of the integrand was taken into account. The lower limit of integration is taken to be zero, followed by doubling of the final result.
 Results. For small values of the broadband parameter, the results of the stochastic and deterministic problems differ little. Examples are presented that are stochastic analogs of harmonic oscillations. For beams under kinematic harmonic disturbances, test examples were performed to determine dispersions and standard deviations.
 The discussion of the results. The results of calculations in the article are presented by curves having numbers that coincide with the numbers of the matrices. The first matrix corresponds to the absolute correlation of disturbances. The second matrix corresponds to the absolute correlation between the first and third, second and fourth disturbances, while these pairs are absolutely uncorrelated. The third matrix describes random perturbations when the indicated pairs, being perfectly positively correlated within, are absolutely perfectly negatively correlated between pairs. The fourth curve corresponds to the case of ideal correlation of the first three disturbances with each other, while the movements of the fourth support are in antiphase with them. In the latter case, the movements of the outer supports are in antiphase with the movements of the middle ones, which favors the greatest bending of the beam. Therefore, the elastic line has a curvature that is significantly greater than the others.

Self-tuning Hamiltonian Monte Carlo for accelerated sampling

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters based on a local loss function that promotes the fast exploration of phase space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein commonly used as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a >100 fold speedup in the optimization of simulation parameters compared to a grid search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times.

VISUAL LIDAR ODOMETRY USING TREE TRUNK DETECTION AND LIDAR LOCALIZATION

Abstract. This paper presents a method of visual LiDAR odometry and forest mapping, leveraging tree trunk detection and LiDAR localization techniques. In environments like dense forests, where smooth GPS signals are unreliable, we employ camera and LiDAR sensors to accurately estimate the robot's position. However, forested or orchard settings introduce unique challenges, including a diverse mixture of trees, tall grass, and uneven terrain. To address these complexities, we propose a distance-based filtering method to extract data composed solely of tree trunk information from 2D LiDAR. By restoring arc data from the LiDAR sensor to its circular shape, we obtain position and radius measurements of reference trees in the LiDAR coordinate system. Then, these values are stored in a comprehensive tree trunk database. Our approach combines visual-based SLAM and LiDAR-based SLAM independently, followed by an integration step using the Extended Kalman Filter (EKF) to improve odometry estimation. Utilizing the obtained odometry information and the EKF, we generate a tree map based on observed trees. In addition, we use the tree position in the map as the landmark to reduce the localization error in the proposed SLAM algorithm. Experimental results show that the loop-closing error ranges between 0.3 to 0.5 meters. In the future, it is expected that this method will also be applicable in the fields of path planning and navigation.

A computational insight on the aromatic amino acids conjugation with [Cp*Rh(H2O)3]2+ by using the meta-dynamics/FMO3 approach

ContextRh(III) complexes demonstrated to exert promising pharmacological effects with potential applications as anti-cancer, anti-bacterial, and antimicrobial agents. One important Rh(III)-ligand is the pentamethylcyclopentadienyl (Cp*) group forming in water the [Cp*Rh(H2O)3]2+ complex. Among of its attractive chemical properties is the ability to react specifically with Tyr amino acid side chain of G-protein–coupled receptor (GPCR) peptides by means of highly chemoselective bioconjugation reaction, at room temperature and at pH 5–6. In this computational work, in order to deepen the mechanism of this chemoselective conjugation, we study the ligand exchange reaction between [Cp*Rh(H2O)3]2+ and three small molecules, namely p-cresol, 3-methylimidazole, and toluene, selected as mimetic of aromatic side chains of tyrosine (Tyr), tryptophan (Trp) and phenylalanine (Phe), respectively. Our outcomes suggest that the high selectivity for Tyr side chain might be related to OH group able to affect both thermodynamic and kinetic of ligand exchange reaction, due to its ability to act as both H bond acceptor and donor. These mechanistic aspects can be used to design new metal drugs containing the [Cp*Rh]2+ scaffold targeting specifically Tyr residues involved in biological/pathological processes such as phosphorylation by means of Tyr-kinase enzyme and protein–protein interactions.MethodsThe geometry of three encounter complexes and product adducts were optimized at the B3LYP//CPCM/ωB97X-D level of theory, adopting the 6-311+G(d,p) basis set for all non-metal atoms and the LANL2DZ pseudopotential for the Rh atom. Meta-dynamics RMSD (MTD(RMSD)) calculations at GFN2-xTB level of theory were performed in NVT conditions at 298.15 K to investigate the bioconjugation reactions (simulation time: 100 ps; integration step 2.0; implicit solvent model: GBSA). The MTD(RMSD) simulation was performed in two replicates for each encounter complex. Final representative subsets of 100 structures for each run were gained with a sampling rate of 1 ps and analyzed by performing single point calculations using the FMO3 method at RI-MP2/6-311G//PCM[1] level of theory, adopting the MCP-TZP core potential for Rh atom.

Traceable Research Data Sharing in a German Medical Data Integration Center With FAIR (Findability, Accessibility, Interoperability, and Reusability)-Geared Provenance Implementation: Proof-of-Concept Study.

Secondary investigations into digital health records, including electronic patient data from German medical data integration centers (DICs), pave the way for enhanced future patient care. However, only limited information is captured regarding the integrity, traceability, and quality of the (sensitive) data elements. This lack of detail diminishes trust in the validity of the collected data. From a technical standpoint, adhering to the widely accepted FAIR (Findability, Accessibility, Interoperability, and Reusability) principles for data stewardship necessitates enriching data with provenance-related metadata. Provenance offers insights into the readiness for the reuse of a data element and serves as a supplier of data governance. The primary goal of this study is to augment the reusability of clinical routine data within a medical DIC for secondary utilization in clinical research. Our aim is to establish provenance traces that underpin the status of data integrity, reliability, and consequently, trust in electronic health records, thereby enhancing the accountability of the medical DIC. We present the implementation of a proof-of-concept provenance library integrating international standards as an initial step. We adhered to a customized road map for a provenance framework, and examined the data integration steps across the ETL (extract, transform, and load) phases. Following a maturity model, we derived requirements for a provenance library. Using this research approach, we formulated a provenance model with associated metadata and implemented a proof-of-concept provenance class. Furthermore, we seamlessly incorporated the internationally recognized Word Wide Web Consortium (W3C) provenance standard, aligned the resultant provenance records with the interoperable health care standard Fast Healthcare Interoperability Resources, and presented them in various representation formats. Ultimately, we conducted a thorough assessment of provenance trace measurements. This study marks the inaugural implementation of integrated provenance traces at the data element level within a German medical DIC. We devised and executed a practical method that synergizes the robustness of quality- and health standard-guided (meta)data management practices. Our measurements indicate commendable pipeline execution times, attaining notable levels of accuracy and reliability in processing clinical routine data, thereby ensuring accountability in the medical DIC. These findings should inspire the development of additional tools aimed at providing evidence-based and reliable electronic health record services for secondary use. The research method outlined for the proof-of-concept provenance class has been crafted to promote effective and reliable core data management practices. It aims to enhance biomedical data by imbuing it with meaningful provenance, thereby bolstering the benefits for both research and society. Additionally, it facilitates the streamlined reuse of biomedical data. As a result, the system mitigates risks, as data analysis without knowledge of the origin and quality of all data elements is rendered futile. While the approach was initially developed for the medical DIC use case, these principles can be universally applied throughout the scientific domain.

FROM MULTIPLE POLYGONS TO SINGLE GEOMETRY: OPTIMIZATION OF POLYGON INTEGRATION FOR CROWDSOURCED DATA

Abstract. Paid crowdsourcing is a popular approach for creating training data in machine learning, but output quality can suffer from various drawbacks, such as noisy data. One solution is to obtain multiple acquisitions of the same dataset and perform integration steps, which can be challenging for geometries such as polygons. In this paper, we propose a raster-based polygon integration approach for the use of crowdsourced data, providing a solution for integrating multiple geometric shapes into single geometries. We analyze the effects of the choice of the integration threshold parameter for different sample sizes on the quality measures intersection over union (IoU) and Hausdorff distance, and provide a recommendation for its optimal selection based on empirical analysis. Additionally, further possibilities to improve integration results are explored, i.e., methods of filtering data before integration by outlier detection.

Numerical verification of the condenser finite volume model

Numerical modelling of vapour compression systems is very useful for performance optimization through the implementation of suitable model-based control applications; in this context the heat exchangers are the most challenging component to devise, due to phase transition and ensuing discontinuities of the physical properties, and one tool which has proven itself suitable for the task is the finite volume method. A numerical verification of a finite volume model of a brazed plate condenser in counterflow arrangement is carried out, employing a fixed timestep solver; some useful guidelines are suggested to properly choose the solver order, the integration step size and the number of grid elements, balancing the accuracy of the predictions with computational time and model stability and flexibility during the transients, with the ultimate goal to provide a model suited for real-time simulations and control-oriented applications.

Implicit integration with a substepping scheme of the zero-elastic range SANISAND-Z model for sand

The SANISAND-Z model is a zero-elastic range boundary surface model. The zero-elastic range makes the model incrementally nonlinear, and consequently, the system of ordinary differential equations of the model formulation is intrinsically implicit. Considering that the calculation results are heavily dependent on the integration step size when the backward Euler method is used to integrate the model, a two-stage diagonally implicit Runge-Kutta algorithm with a substepping scheme is proposed in this study. The substepping scheme is achieved by an embedded local integration error estimate. Based on the user-defined material subroutine interface UMAT of ABAQUS software, the SANISAND-Z model is numerically implemented with the proposed numerical integration algorithm. By monotonic and cyclic element tests and the case of strip footing loading, the performance of the proposed numerical integration algorithm is thoroughly investigated. The results show that the proposed algorithm is more accurate and efficient than the backward Euler method.

Simulating ionization feedback from young massive stars: impact of numerical resolution

ABSTRACT Modelling galaxy formation in hydrodynamic simulations has increasingly adopted various radiative transfer methods to account for photoionization feedback from young massive stars. However, the evolution of H ii regions around stars begins in dense star-forming clouds and spans large dynamical ranges in both space and time, posing severe challenges for numerical simulations in terms of both spatial and temporal resolution that depends strongly on gas density (∝n−1). In this work, we perform a series of idealized H ii region simulations using the moving-mesh radiation-hydrodynamic code arepo-rt to study the effects of numerical resolution. The simulated results match the analytical solutions and the ionization feedback converges only if the Strömgren sphere is resolved by at least 10–100 resolution elements and the size of each time integration step is smaller than 0.1 times the recombination time-scale. Insufficient spatial resolution leads to reduced ionization fraction but enhanced ionized gas mass and momentum feedback from the H ii regions, as well as degrading the multiphase interstellar medium into a diffuse, partially ionized, warm (∼8000 K) gas. On the other hand, insufficient temporal resolution strongly suppresses the effects of ionizing feedback. This is because longer time-steps are not able to resolve the rapid variation of the thermochemistry properties of the gas cells around massive stars, especially when the photon injection and thermochemistry are performed with different cadences. Finally, we provide novel numerical implementations to overcome the above issues when strict resolution requirements are not achievable in practice.

REDUCTION OF HEAT GAINS TO GEOTHERMAL HEAT EXCHANGERS IN LONG-TERM OPERATION

Link for citation: Polovnikov V.Yu., Shelemekhova S.D. Reduction of heat gains to geothermal heat exchangers in long-term operation. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 9, рр. 18-24. In Rus. The relevance of the research is caused by the colossal energy potential of geothermal and petrothermal energy. It is designed to stimulate research and development in the field of geothermal technologies. The development of technologies for the use of geothermal and petrothermal energy in the Russian Federation is reduced by some circumstances. These main reducing factors are competition from traditional energy, problems with the legal framework and the lack of relevant areas of research and development. Currently, there is a backlog of Russia in the field of development of geothermal resources from the world level. The main aim of the study is to evaluate the effect of condensation in the design of a geothermal heat exchanger on the change in heat inflows to it. The object of the research is a typical design of a geothermal heat exchanger consisting of a metal pipeline and a cement casing. Methods. Numerical analysis of heat and mass transfer was executed with rational values of the grid parameters and the time integration step. The assessment of the reliability of the results of the work was carried out by testing on the example of heat transfer problems, the numerical methods used and elements of the developed algorithms for solving boundary value problems of heat and mass transfer, checking the conservatism of difference schemes, and comparing with known data. The finite difference method and the implicit difference scheme were used. The peculiarity of problem solving was the discontinuity of the thermophysical characteristics at the contact boundaries between the layers and the presence of nonlinearity in the boundary condition. Results. The authors have carried out the numerical study of the effect of steam condensation in the design of a geothermal heat exchanger on the reduction of heat inflows in the system under consideration. It was found that steam condensation leads to a decrease in heat gain by 4,55–31,19 %. It is shown that the use of relatively simple heat transfer models makes it possible to predict the change in heat inflows to a geothermal heat exchanger under conditions of steam condensation in its structure during long-term operation.

Strengthening the Institutional Independence of the Court in the System of European Integration Steps of Ukraine

The article is devoted to the study of European standards of judicial independence. The subject of the study is the institution of court independence and specific measures to improve its legal support in Ukraine in accordance with European standards. The purpose of the article is to determine the following judicial reform measures aimed at institutional and legal harmonization of Ukrainian legislation with the standards of the European Union. The research uses dialectical, systematic analysis and synthesis, comparison and legal modeling methods of scientific knowledge. Acquiring the status of a candidate country in the EU obliges Ukraine to carry out a number of transformations of social and political institutions, and judicial reform is one of them. This will require systemic measures, and not just amendments to legislation aimed at harmonizing national legal norms with European standards. It is emphasized that despite the ongoing judicial reform, the goal of an effective court has not been achieved: the level of public trust in the court is still low. The author predicts that if only point changes in judicial legislation are started now, the result will be the same as during the previous steps of judicial reform. It is necessary to start with the construction of the foundation for an effective judicial system, which is the independence of the court. Analyzing the European standards of an independent court and the practices of the EU institutions regarding the assessment of the impact of various indicators on the general assessment of the assurance of court independence, taking into account the current and urgent problems of the judicial system of Ukraine, the author makes a number of proposals for improving domestic legislation and practice aimed at strengthening the independence of the court, which the author calls fundamental the value of a democratic state, a prerequisite for an effective judicial protection system.

PC-Reg: A pyramidal prediction–correction approach for large deformation image registration

Deformable image registration plays an important role in medical image analysis. Deep neural networks such as VoxelMorph and TransMorph are fast, but limited to small deformations and face challenges in the presence of large deformations. To tackle large deformations in medical image registration, we propose PC-Reg, a pyramidal Prediction and Correction method for deformable registration, which treats multi-scale registration akin to solving an ordinary differential equation (ODE) across scales. Starting with a zero-initialized deformation at the coarse level, PC-Reg follows the predictor–corrector regime and progressively predicts a residual flow and a correction flow to update the deformation vector field through different scales. The prediction in each scale can be regarded as a single step of ODE integration. PC-Reg can be easily extended to diffeomorphic registration and is able to alleviate the multiscale accumulated upsampling and diffeomorphic integration error. Further, to transfer details from full resolution to low scale, we introduce a distillation loss, where the output is used as the target label for intermediate outputs. Experiments on inter-patient deformable registration show that the proposed method significantly improves registration not only for large but also for small deformations.