Methods and apparatus for determining bonds in particle trajectories

Abstract

This disclosure relates to a method (100) for determining bonds in particle trajectories, comprising the steps of: obtaining (101) a dataset of particle trajectories in a material system; dynamically identifying bonds between particles in the material system (102), wherein dynamically identifying bonds includes: selecting (103) candidate bonds comprising a pair of particles (10, 11). A candidate bond (104) is determined to be bonded if: during a first predetermined time period (t1), the pair of particles (10, 11) is closer than a predetermined maximum distance based on the combination of particle radii (r1, r2) of the pair of particles (10, 11); during a second predetermined time period (t2), the average distance (d') between the pair of particles (10, 11) is within a tolerance (t') associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pair of particles (10, 11), or a measure of the nearest neighbor distance or equilibrium bond length of the pair of particles (10, 11); and during a third predetermined time period (t3), the first particle (10) in the candidate bond is not present in the repellent (15) associated with the second particle (11) and any other particle (12) in the candidate bond, or the first particle in the candidate bond satisfies the bond length criterion if it is present in the repellent (15).

Description

Technical Field

[0001] This disclosure relates to a method for determining bonds in a particle trajectory and predicting forces in a particle trajectory. Background Technology

[0002] Currently, many technically relevant materials and liquids are complex in terms of their often disordered and / or dynamic intermolecular structures and dynamics. Even for simpler materials, their fabrication and manipulation typically involve some degree of complexity.

[0003] The structure of a material system can be defined, for example, by the bonds between its constituent particles.

[0004] Currently, there are experimental methods available on the market designed to determine the structure and dynamics of material systems, such as X-ray diffraction, vibrational spectroscopy, electrical impedance spectroscopy, and electrochemical techniques.

[0005] However, the experimental techniques mentioned cannot directly address the complexity issue that these techniques either predict very local structures or only crystal structures. Furthermore, these techniques cannot reliably and rapidly capture the explicit dynamics, structure, and bonds between atoms in a material system. The same applies to quantum chemical modeling methods, such as Hartree-Fock theory, density functional theory, and coupled-cluster calculations. While molecular dynamics and similar techniques can explicitly capture atomic motions at the necessary scales, currently available analytical techniques may be unable to capture higher-level (e.g., supramolecular) structures and their dynamics.

[0006] In complex material systems, atomic trajectories are often intricate and challenging to analyze, particularly concerning supramolecular structures and dynamics. Therefore, dynamically characterizing and identifying the bonds between atoms in a material system will enable the calculation of many physicochemical properties of the system and an understanding of how these properties arise from molecular-scale dynamics.

[0007] Therefore, there is a gap in the field of analyzing the disordered structure and dynamics of systems, and more specifically, it is necessary to determine the bonds between atoms in a material system.

[0008] Therefore, there is a need to determine bonds in atomic orbitals in a rapid, efficient, and reliable manner in order to further predict the physicochemical properties of material systems. Consequently, there is room in the field to explore methods that provide rapid, efficient, and reliable methods for determining bonds in material systems.

[0009] While some known solutions work well in certain situations, there is a need to provide methods and apparatus that meet the above requirements. Summary of the Invention

[0010] Therefore, the purpose of this disclosure is to provide methods and apparatus for mitigating, alleviating or eliminating one or more of the defects and disadvantages identified above.

[0011] This objective is achieved by means of methods for determining bonds in the trajectory of particles (e.g., atoms), computer-readable storage media, and apparatus thereof.

[0012] This disclosure provides a method comprising the following steps: First, obtaining a dataset of particle trajectories in a material system, such as a condensed matter system. Then, dynamically identifying bonds between particles in the material system. Dynamically identifying bonds includes: selecting candidate bonds comprising a pair of particles, and determining the candidate bond as bonded if: during a first predetermined time period, the pair of particles is closer than a predetermined maximum distance based on a combination of their particle radii; and during a second predetermined time period, the average distance between the pair of particles is within a tolerance associated with at least one of the following: the peak value of the partial radial distribution function (pRDF) of the pair of particles, or a measure of the nearest neighbor distance or equilibrium bond length of the pair of particles. Furthermore, during a third predetermined time period, the candidate bond is bonded if the first particle of the candidate bond is not present in an exclusion body associated with the second particle and any other particle in the candidate bond, or if the first particle of the candidate bond is present in the exclusion body, then a bond length criterion is satisfied. The exclusion body may be in the form of a three-dimensional semi-infinite cone or a central spherical cube.

[0013] This method offers the benefit of reliably and efficiently determining bonds in material systems. This has the advantage of forming a basis for studying explicit representations of the structure and dynamics of material systems. The method provides multiple criteria that must be met to identify candidate bonds as bonds, allowing for high reliability and accuracy. Furthermore, the method enables the determination of bonds relative to a time period, further providing a more reliable and accurate approach. The criteria consider both the distances between particles of the candidate bond and the distances of any other particle relative to the candidate bond during a time period suitable for the dynamic system.

[0014] A bond length criterion can be satisfied if the first length between particles in a candidate bond is less than a predetermined factor multiplied by a second length, wherein the second length is defined by the distance between a pair of particles associated with the repulsive body.

[0015] Therefore, this allows for alternative means to provide reliability in determining particle bonds. This prevents candidate bonds from being incorrectly identified as unbonded simply because they are present in a repellent. The reliability and accuracy of the method are further improved by also considering bond length criteria in the case of candidate bonds within a repellent.

[0016] The method may also include the following steps: determining the bond lifetime if the candidate bond is determined to be a bond.

[0017] The benefit of this step is that it allows the method to take into account the complexity and dynamic properties of the material system. Determining the bond lifetime provides alternative means of obtaining the physicochemical properties of the system.

[0018] The method may further include the step of determining at least one bond map based on the identified bonds in the material system. The at least one bond map may be a time-dependent bond map.

[0019] The benefit of identifying at least one bond graph is that it enables detailed representation and classification of the structures and different types of particles present in a material system, with the position in the bond graph also included in the type definition.

[0020] The method may also include the following steps: characterizing local results or global structure based on the partitioning of at least one bond graph, and predicting the physicochemical properties of the material system based on the local results or global structure.

[0021] This step offers the benefit of allowing for the representation of the structure, which facilitates further analysis / work and uniquely promotes the understanding of the structural, kinetic, and physicochemical properties arising from the supramolecular structure and interactions.

[0022] The bond graph can be divided into subgraphs according to a first representation model or a second representation model, wherein the first representation model includes dividing the bond graph into connected components, and the second representation model includes dividing the bond graph into extended neighborhoods defined by all vertices and edges such as at least one of the central particle or motif up to the maximum graph distance.

[0023] The benefit of this step is that bond graphs can be arranged more easily by dividing them into different representation models corresponding to specific examples of the structure, and examples can be categorized into different types that can be studied across examples. For example, each representation model can point to a specific type of structure, such as a permeable network or a small isolating component, or the representation models can complement each other, enabling a deeper understanding of individual material systems.

[0024] The average distance d' between a pair of particles (see Figures 4a to 4b It can satisfy:

[0025]

[0026] Where α is the tolerance, r peakIt is the peak value in the partial radial distribution function pRDF, or other measures such as nearest neighbor distance or equilibrium bond length, and d ij (t) is the distance as a function of time t.

[0027] The advantage of doing this is that the average distance d' can be obtained by also using time and tolerance as factors that make it more suitable for complex dynamic systems.

[0028] The partial radial distribution function pRDF can be constrained by the following:

[0029]

[0030] Where n(r) is the number density of the neighborhood of type j at a distance r from the particle of type i, and the expression is normalized by the average volume number density n0 of type j.

[0031] A computer-readable storage medium is also provided, which stores one or more programs configured to be executed by one or more control circuits of an electronic device, said one or more programs including instructions for performing the methods disclosed herein.

[0032] An electronic device is also provided, comprising: one or more control circuits; and a memory storing one or more programs configured to be executed by the one or more control circuits, the one or more programs including instructions for performing the methods disclosed herein.

[0033] According to some aspects of this disclosure, a method for determining bonds in particle trajectories is also provided, the method comprising the steps of: obtaining a dataset of particle trajectories in a material system. Furthermore, the method comprises the step of: dynamically identifying bonds between particles in the material system. Furthermore, the method comprises determining at least one bond graph based on the identified bonds in the material system. Furthermore, the method comprises characterizing at least one interaction type of at least one particle in the at least one bond graph based on the partitioning of the at least one bond graph. Furthermore, the method provides a predefined scheme including average force field data, which is data associated with a force field model acting on each characterized interaction type of particle.

[0034] The advantages of this method are that it provides a cost-effective approach to predict the forces acting on particles in a system without explicitly calculating costly, long-range interactions, while maintaining the accuracy of the (training) data. Furthermore, it enables the timely propagation of particle trajectories. Moreover, this method can accurately and rapidly determine the bonds in particle trajectories not only in real-time within the system but also for future points in time within the system.

[0035] The predefined scheme can be a lookup table, a function, or any other form of lookup model. Therefore, after identifying each interaction type, the method can use the predefined scheme to provide and determine the mean force field data for a specific interaction.

[0036] The method may also include the following steps: propagating the trajectory of the identified bonds in the material system based on a predefined scheme.

[0037] The step of dynamically identifying bonds between particles in a material system may include selecting candidate bonds that consist of a pair of particles. Furthermore, candidate bonds are identified as bonded in the following cases:

[0038] i. Within a first predetermined time period, based on the combination of the particle radii of the pair of particles, the pair of particles are closer than a predetermined maximum distance;

[0039] ii. During the second predetermined time period (t2), the average distance (d') between the pair of particles (10, 11) is within a tolerance (t') associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pair of particles (10, 11), or a measure of the nearest neighbor distance or balance bond length of the pair of particles (10, 11); and

[0040] iii. During the third predetermined time period (t3), the first particle (10) of the candidate bond is not present in the repellent (15) associated with the second particle (11) and any other particle (12) in the candidate bond, or the first particle (10) of the candidate bond satisfies the bond length criterion if it is present in the repellent (15).

[0041] Furthermore, average force field data for each interaction type can be obtained / determined from the distribution of generalized forces on the generalized force field description coordinates, wherein each interaction type is associated with at least one generalized force field description coordinate.

[0042] In other words, for each identified interaction type, the method can obtain a generalized force distribution for a specific interaction type, wherein the method determines a mean or a dataset of mean values ​​based on the distribution.

[0043] The average distribution can be at least one of the mean value of the force distribution, the modal value of the force distribution, or the median value of the force distribution, or any combination thereof.

[0044] The propagation step may include time integration of the material system from a first time point to a second time point. This allows the method to accurately simulate the future state of the material system.

[0045] The interaction type can be at least one of two-body or non-bonded interactions, three-body or non-bonded interactions, four-body or non-bonded interactions, and n-body or non-bonded interactions, where n is any non-negative integer. Therefore, this method offers the advantage of identifying multiple different interaction types as well as identifying non-bonded interactions, resulting in a more accurate method. The interaction type can also be any other suitable interaction type.

[0046] The method may also include the following steps: using force field data to generate a smooth function that depends on at least one generalized force field describing coordinate. Attached Figure Description

[0047] The present disclosure will be described in more detail below in a non-limiting manner and with reference to the exemplary embodiments and experiments shown in the accompanying drawings, in which:

[0048] Figure 1 A method for determining bonds in a particle trajectory according to an embodiment of this disclosure is illustrated in flowchart form.

[0049] Figure 2 The steps for determining candidate keys as combinations are illustrated in the form of a decision tree.

[0050] Figure 3a This shows a pair of particles under the condition of satisfying standard i.

[0051] Figure 3b This shows a pair of particles without satisfying criterion i.

[0052] Figure 4a An example of the partial radial distribution function of a pair of particles associated with Standard II is shown.

[0053] Figure 4b The diagram shows a pair of particles in Figure 4a The curve within the tolerance of pRDF in the graph

[0054] Figure 5 The diagram shows the repulsion cone, candidate bonds, and additional particles associated with Standard III.

[0055] Figure 6 A method for determining bonds in a particle trajectory according to an embodiment of this disclosure is illustrated in flowchart form.

[0056] Figure 7 A graph showing the lifespan of the display keys is shown.

[0057] Figure 8 An electronic device according to an embodiment of the present disclosure is illustrated schematically.

[0058] Figure 9A method for determining bonds in a particle trajectory, according to one aspect of this disclosure, is schematically illustrated in the form of a flowchart.

[0059] Figure 10 A graph showing the force distribution for all values ​​of the generalized coordinates; and

[0060] Figure 11 A bonding diagram according to an embodiment of this disclosure is shown. Detailed Implementation

[0061] In the following detailed description, some embodiments of the present disclosure will be described. However, it should be understood that, unless otherwise specifically indicated, features of different embodiments are interchangeable between the embodiments and can be combined in different ways. Although numerous specific details are set forth in the following description to provide a more thorough understanding of the provided methods and apparatus, it will be apparent to those skilled in the art that the methods and apparatus can be implemented without these details. In other instances, well-known structures or functions have not been described in detail so as not to obscure the present disclosure.

[0062] In the following description of exemplary embodiments, the same reference numerals denote the same or similar parts.

[0063] In this disclosure, particles, material systems, and bonds are defined in their broadest sense. A particle can be any number of matter that can distribute the center of mass at any point in time, including but not limited to atoms, ions, electrons, holes, molecules, functional groups, beads, particles, colloids, vesicles, and rigid bodies. A material system can be any system composed of multiple interacting particles. A bond between a pair of particles can be an interaction that causes them to move together as a cohesive unit. The concept of interaction can also include effective interactions such as a steric effect, aggregation effects of interactions between other particles, or even spatial and temporal correlations due to initial conditions or external causes. Types of bonds include, but are not limited to: covalent bonds, ionic bonds, metallic bonds, van der Waals interactions, spatial confinement, any form of adhesion, and any form of electromagnetic interaction. Capturing the structure and dynamics of complex material systems, or even complex processes in simpler material systems, can often be challenging. This disclosure is directed to condensed matter systems of atoms, ions, and molecules, but is equally applicable to the broader categories of particles, interactions, and material systems described herein.

[0064] The term "bond candidate time" refers to a time period during which a pair of particles can be conceived to be bound together based on their relatively small distance.

[0065] The term "distance-average time" refers to a time period (a subset of the candidate bond times) during which it is meaningful to calculate the time-averaged distance between a pair of particles without the average being biased toward a larger value due to the possible orientations of the pair of particles initially approaching each other and eventually moving away from each other.

[0066] The term "bond repulsion time" refers to the time period during which it is determined whether candidate bonds are evenly located within any repellent.

[0067] The term "bond lifetime" refers to the time between bond formation (i.e., being determined to be bonded) and bond breakage.

[0068] The term "motif" refers to a single particle or a group of particles that may have a defined internal bond graph topology.

[0069] The term "material system" refers to a system consisting of multiple particles that interact or effectively interact in some way, including but not limited to being in a solid or liquid state. The material systems disclosed herein may be condensed matter systems.

[0070] Figure 1 A method 100 for determining bonds according to an embodiment of the present disclosure is illustrated. Method 100 includes the step of: obtaining a dataset of particle trajectories in a material system 101.

[0071] Furthermore, the bonds 102 between particles in the material system are dynamically identified, wherein the step of dynamically identifying bonds 102 includes: selecting 103 candidate bonds consisting of a pair of particles 10, 11. Candidate bonds are determined 104 to be bonded in the following cases (see Figures 3 to 3 for details related to i to iii). Figure 5 ):

[0072] i. Within the first predetermined time period t1, based on the particle radii r1 and r2 of the pair of particles (e.g., ... Figures 3a to 3b The combination of particles 10 and 11 (as shown) is such that the distance between them is greater than the predetermined maximum distance d. max (see Figures 3a to 3b Closer;

[0073] ii. During the second predetermined time period t2, the average distance d' between the pair of particles 10 and 11 is within a tolerance t' associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pair of particles 10 and 11, or a measure of the nearest neighbor distance or balance bond length of the pair of particles 10 and 11; and

[0074] iii. During the third predetermined time period t3, the first particle 10 in the candidate bond is not present in the repellent 15 associated with the second particle 11 and any other particle 12 in the candidate bond, or the first particle 10 in the candidate bond satisfies the bond length criterion if it is present in the repellent 15.

[0075] The term "criteria" refers to the three steps required to determine a candidate key for bonding according to the 104-step determination process. These criteria are denoted as i through iii in this disclosure.

[0076] The term "particle" can refer to an atom. Accordingly, this method can be targeted at identifying the bonds between atoms in a material system. Therefore, Figure 1 The pair of particles 10 and 11 shown can be a pair of atoms.

[0077] The first predetermined time period t1 can be the bond candidate time, which is defined as a time period during which it is conceivable that the pair of particles 10 and 11 will be bonded based on their distance being below a cutoff value.

[0078] The second predetermined time period t2 can be the distance average time, which is limited to a subset of the candidate bond times. Within this time period, the time-averaged distance between the pair of particles 10 and 11 is calculated without being biased towards a larger value due to the possible initial approach and final departure of the pair of particles towards each other (e.g., ...). Figure 4b (As shown).

[0079] The third predetermined time period t3 can be the bond repulsion time, which is defined by the following time period, during which it is determined whether candidate bonds 10 and 11 are evenly located within any repellent.

[0080] The step of dynamically identifying key 102 can be performed iteratively, allowing multiple keys to be identified over a longer time period. Furthermore, the method 100 can select 103 multiple candidate keys and simultaneously perform determination step 104 on each individual candidate key.

[0081] Figure 2 The steps for determining candidate keys 104 as combinations are disclosed in more detail in the form of a decision tree executed by method 100. For example... Figure 2 As shown, criteria / conditions i to iii must be met in order to determine candidate keys 10 and 11 as combined. Furthermore, in Figure 2 In this process, criteria i to iii need to be satisfied in a specific order in order to determine the candidate keys as combined. However, according to some implementations, criteria i to iii can be satisfied in any order.

[0082] Figure 3a and Figure 3bThe standard i in the steps of determining 104 is shown in more detail, demonstrating... Figure 3a In the first case, within a first predetermined time period, based on the combination of particle radii r1 and r2 of a pair of particles, the pair of particles is closer than a predetermined maximum distance dmax. Figure 3a Satisfy d max <C(r1+r2). C can be a coefficient in the range of 0.1 to 10. The particle radii r1 and r2 can be van der Waals radii, ionic radii, covalent radii, metallic radii, or cutoff values ​​based on electron density.

[0083] Figure 3b This shows the second case where condition i is not satisfied. In other words, Figure 3a Particles 10 and 11 in the sample can be combined because i in the standard was passed in step 104. However, in Figure 3b In this context, since criterion i is not met, particles 10 and 11 can be determined to be non-bound. Therefore, in... Figure 3b In the middle, d max <C(r1+r2).

[0084] Figure 4a A portion of criterion ii is shown in step 104, where the partial radial distribution function of the pair of particles (i.e., candidate bonds) can be seen. Therefore, criterion ii is satisfied if the average distance d′ between the pair of particles is within the tolerance t′ associated with the peak p1 of the pRDF seen in Figure 4. From Figure 4b It can be seen from this that the average distance d′ is in Figure 4a This is within the tolerance mentioned above. Therefore, the average distance d′ is not within... Figure 4a Within the tolerance t′ mentioned above, candidate keys are determined to be unbonded. The tolerance t′ can be associated with the first peak of the pRDF. This tolerance can be limited by 1% to 200% of the half-width at half the maximum value of the pRDF.

[0085] Figure 5 The case relating to criterion iii in step 104 is shown, where candidate bonds 10, 11 and a repellent 15 associated with one of the particles 11 in the candidate bonds and any other particle 12 can be seen. It should be noted that if candidate bonds 10, 11 are present in the repellent 15 but meet the bond length criterion, candidate bonds 10, 11 can still be bonded. The other particle 12 can be another particle bonded to one of the particles in candidate bonds 10, 11. The other particle 12 can be another particle previously identified as bonded by means of method 100. The repellent 15 is three-dimensional (in...). Figure 5 (Not explicitly seen in the text). Furthermore, the term "body" is preferably a semi-infinite cone (e.g., ...). Figure 5(As seen in the image), but it can also be any other suitable form, such as a cone or a central sphere with a finite height. For example... Figure 5 As seen, the repulsion cone 15 can be defined by having an end 13 associated with the center of one of the candidate particles 11, an axis in the direction of particle 12 different from that of candidate particle 10 (not explicitly shown, but in the direction of L2), and also having a predetermined angle. This angle can be in the range of 30° to 120°.

[0086] A bond length criterion is satisfied if the first length L1 between particles 10 and 11 in candidate bonds 10 and 11 is less than a predetermined coefficient multiplied by a second length L2, where the second length L2 is defined by the length between a pair of particles 11 and 12 associated with repulsion 15. This coefficient can be in the range of 1.0 to 2.0. Figure 5 In this case, the first particle 10 is within the repulsion cone 15, so criterion iii can only be satisfied if the first length L1 between particles 10 and 11 in the candidate bond is less than a predetermined coefficient multiplied by the second length L2. If the center of mass 16 of the particle is within the repulsion cone, then the particle can be confined to being within the repulsion cone.

[0087] Figure 6 The method 100 is shown to further include the following step: if candidate bonds 10 and 11 are combined, then determine the bond lifetime 105. The bond lifetime can be determined by starting from the average bond time and extending in both directions until a distance greater than or equal to the maximum distance within the average bond time (e.g., ...). Figure 7 (As shown).

[0088] Reference Figure 6 The method 100 also includes the step of determining at least one bond graph 106 based on the identified bonds in the material system. Figure 6 The method also includes the following steps: characterizing the local structure 107 based on the partitioning of at least one bond graph, and predicting the physicochemical properties of the material system 108 based on the local structure.

[0089] The bond graph can be partitioned according to a first representation model or a second representation model, wherein the first representation model includes partitioning the bond graph into connected components, and the second representation model includes partitioning the bond graph into a graph neighborhood defined by a maximum graph distance from at least one of the central particle or motif.

[0090] The term "extended neighborhood" refers to a subgraph of a larger graph that includes all vertices from the central radix up to a predetermined graph distance, as well as the edges between these vertices.

[0091] The term "bond graph" refers to a graph with vertices, where the vertices are particles or groups of particles, and the edges can be undirected, which are the bonds between particles or groups of particles.

[0092] The term "graph distance" is defined as the minimum number of edges required to connect two vertices in a graph.

[0093] The average distance d' between a pair of particles can satisfy:

[0094]

[0095] Where α is the tolerance t', r peak It is the peak value in the partial radial distribution function pRDF, or other measures such as nearest neighbor distance or equilibrium bond length, and d ij (t) is the distance as a function of time t.

[0096] Furthermore, the partial radial distribution function pRDF can be constrained by the following...

[0097]

[0098] Where n(r) is the number density of particles or motifs of type j at a distance r from particles of type i, and the expression is normalized by the average volumetric number density n0 of type j.

[0099] Figure 8 An electronic device 1 is schematically depicted, comprising: a control circuit 2; and a memory device 3 storing one or more programs configured to be executed by one or more control circuits 2, the one or more programs comprising instructions for performing the method 100 disclosed herein.

[0100] Memory device 2 may include any form of volatile or non-volatile computer-readable memory, including but not limited to permanent storage devices, solid-state memory, remotely mounted memory, magnetic media, optical media, random access memory (RAM), read-only memory (ROM), large-scale storage media (e.g., hard disk), removable storage media (e.g., flash drives, compact discs (CDs), or digital video discs (DVDs)), and / or any other volatile or non-volatile, non-transitory device-readable and / or computer-executable memory device that stores information, data, and / or instructions that can be used by each associated control circuit 2. Memory device 3 may store any suitable instructions, data, or information, including computer programs, software, applications including logic, rules, codes, tables, etc., and / or other instructions that can be executed and utilized by the control circuits. Memory device 3 may be used to store any calculations performed by the control circuit 2 and / or any data received via an interface. In some embodiments, each control circuit 2 and each memory device 3 may be considered integrated.

[0101] Each memory device 3 may also store data that can be retrieved, manipulated, created, or stored by the control circuitry 2. The data may include, for example, local updates, parameters, training data for optimizing the method 100 disclosed herein, learning models, and other data. The data may be stored in one or more databases. One or more databases may be connected to a server via a high-bandwidth field network (FAN) or a wide area network (WAN), or via a communication network.

[0102] The control circuit 2 may include, for example, one or more central processing units (CPUs), graphics processing units (GPUs) dedicated to performing calculations, and / or other processing devices.

[0103] The memory device 3 may include one or more computer-readable media and may store information accessible to the control circuitry, including instructions / programs that can be executed by the control circuitry 2.

[0104] The instructions executable by the control circuit 2 may include instructions for performing method 100 according to any aspect of this disclosure. Each control circuit 2 may be configured to perform any step disclosed in this disclosure, such as the steps in method 100.

[0105] A computer-readable storage medium is also provided, which stores one or more programs configured to be executed by one or more control circuits of electronic device 1, said one or more programs including instructions for performing the method 100 disclosed herein. The electronic device may be... Figure 8 Electronic devices in the middle.

[0106] Figure 9 A method 200 for determining bonds (and predicting forces) in particle trajectories, according to one aspect of this disclosure, is illustrated. Method 200 includes the steps of: 201 obtaining a dataset of particle trajectories in a material system; dynamically identifying bonds between particles in the material system; 202 further including: determining 203 at least one bond graph based on the identified bonds in the material system; 204 characterizing at least one interaction type of at least one particle in the at least one bond graph based on the partitioning of the at least one bond graph; 205 providing a predefined scheme including average force field data, which is data related to the force field acting on each particle of the characterized interaction type; and 206 further including the step of propagating the identified bond trajectories in the material system based on the predefined scheme.

[0107] Figure 9It is also shown that the step of dynamically identifying bonds 202 between particles in a material system may include: selecting candidate bonds 202' comprising a pair of particles, and determining the candidate bonds 202" as bonded if certain criteria are met.

[0108] like Figure 9 As shown, method 200 may further include the step of: using the (205') force field data to generate a smooth function dependent on at least one generalized force field descriptor coordinate, by means of one or more learning algorithms, statistical methods, interpolation methods, extrapolation methods, or any combination thereof. The learning algorithms, statistical methods, interpolation methods, or extrapolation methods may be based on Bayesian learning, neural networks, linear regression, nonlinear regression, maximum likelihood estimation, combinations thereof, or any other suitable method.

[0109] The standards to be met are Figures 2 to 5 The details are shown in the disclosure, and the same steps, means, and advantages as previously discussed in this disclosure may be made public, according to the following criteria:

[0110] i. During the first predetermined time period (t1), based on the particle radius (r1, r2) of a pair of particles (10, 11),

[0111] The combination of r2) brought the pair of particles (10, 11) closer than the predetermined maximum distance;

[0112] ii. During the second predetermined time period (t2), the average distance (d') between the pair of particles (10, 11) is within a tolerance (t') associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pair of particles (10, 11), or a measure of the nearest neighbor distance or equilibrium bond length of the pair of particles (10, 11); and

[0113] iii. During the third predetermined time period (t3), the first particle (10) of the candidate bond is not present in the repellent (15) associated with the second particle (11) and any other particle (12) of the candidate bond, or the first particle of the candidate bond is present in the repellent (15).

[0114] Under the condition that the bond length meets the standard.

[0115] Figure 10A schematic diagram of generalized forces associated with interaction types described by generalized coordinates q is shown. For each value of coordinate q, there exists a distribution of force F, which can be assumed to be Gaussian. Therefore, for all values ​​of q, there exists a distribution that collectively forms a two-dimensional histogram. In other words, the histogram is the projection / distribution of the generalized forces acting on all particles involved in the interaction type relative to the generalized coordinates q describing the interaction. Based on the two-dimensional histogram, an average value can be determined and stored in a lookup table, which may or may not be used to generate a smoothing function through, for example, Bayesian learning, neural networks, or linear or nonlinear regression, such that for each interaction type, there exists a stored average value (or a set of values), which can then be used to propagate the material system. According to this disclosure, the lookup table can correspond to a predefined scheme. Accordingly, the combination of interaction type and average force field value allows for the propagation of the system. The reference numeral A indicates the set of generalized force distributions F.

[0116] The term "force field" can refer to the type of force between atoms within all types of bonded and unbonded interactions, including its lookup representation. Therefore, "force field" can refer to tensile force, bending force, appropriate and inappropriate torsional force, van der Waals force, electrostatic force, or other force terms, and any combination thereof.

[0117] The average force field data for each interaction type is obtained from the distribution of generalized forces on the generalized force field description coordinates, where each interaction type is associated with at least one generalized force field description coordinate.

[0118] The mean force field data can be at least one of the mean value of the force distribution, the modal values ​​of the force distribution, or the median value of the force distribution, or any combination thereof. The data can be a set of mean values, a set of modal values, or a set of medians.

[0119] The propagation steps 206 may include: performing time integration on the material system from a first time point to a second time point.

[0120] The interaction type can be at least one of two-body bonded or unbonded interaction, three-body bonded or unbonded interaction, four-body bonded or unbonded interaction, and n-body bonded and unbonded interaction, where n is any non-negative integer. In other words, these interaction types can be interactions between the first atom and at least one additional atom.

[0121] Figure 11 A bond diagram according to some embodiments is shown, wherein bonds are dynamically identified in the particle trajectories of the material system and displayed in the bond diagram. Figure 11 The bond diagram shown is a simplified view for illustrative purposes and does not limit the scope of this disclosure.

Claims

1. A method (100) for determining bonds in a particle trajectory, comprising the following steps: - Obtain a dataset of particle trajectories in a (101) material system; - Dynamically identify bonds between particles in the material system (102), wherein dynamically identifying bonds includes: - The selection (103) includes a pair of candidate bonds (10, 11); - The candidate key is determined to be combined (104) in the following cases: i. During a first predetermined time period (t1), based on the combination of particle radii (r1, r2) of the pair of particles (10, 11), the pair of particles (10, 11) is closer than a predetermined maximum distance; ii. During the second predetermined time period (t2), the average distance (d') between the pairs of particles (10, 11) is within a tolerance (t') associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pairs of particles (10, 11), or a measure of the nearest neighbor distance or equilibrium bond length of the pairs of particles (10, 11); and iii. During a third predetermined time period (t3), the first particle (10) of the candidate bond is not present in the repellent (15) associated with the second particle (11) and any other particle (12) in the candidate bond, or the first particle of the candidate bond satisfies the bond length criterion if it is present in the repellent (15).

2. The method (100) according to claim 1, wherein, The bond length criterion is satisfied if the first length (L1) between the pairs of particles (10, 11) in the candidate bond is less than a predetermined factor multiplied by a second length (L2), wherein the second length (L2) is defined by the length between the pairs of particles associated with the repulsion body.

3. The method (100) according to claim 1 or 2 further comprises the following step: - If the candidate bond is bonded, determine the (105) bond lifetime.

4. The method (100) according to claim 1 further includes the following step: - Determine (106) at least one bond graph based on the identified bonds in the material system.

5. The method (100) according to claim 4, further comprising the following step: - Characterize (107) particle type or local structure or global structure based on the partitioning of at least one bond graph; - Predict the physicochemical properties of the material system based on the particle type, the local structure, or the global structure.

6. The method (100) according to claim 4, wherein, The bond graph is partitioned according to a first representation model or a second representation model, wherein the first representation model includes partitioning the bond graph into connected components, and the second representation model includes partitioning the bond graph into graph neighborhoods defined by vertices at least one of the central particle or motif up to the maximum graph distance and the edges between said vertices.

7. The method (100) according to claim 1, wherein, The average distance (d') between a pair of particles satisfies: ， Where α is the tolerance, r peak It is the peak value in the partial radial distribution function pRDF, or other measures such as nearest neighbor distance or equilibrium bond length, where T represents the second predetermined time period, and d ij (t) is the distance as a function of time t.

8. The method (100) according to claim 1, wherein, The partial radial distribution function pRDF is ， Wherein, n(r) is the number density of particles or motifs of type j at a distance r from particles of type i, and the expression is normalized by the average volumetric number density n0 of type j.

9. A computer-readable storage medium storing one or more programs configured to be executed by one or more control circuits of an electronic device, said one or more programs comprising instructions for performing the method (100) according to any one of claims 1 to 8.

10. An electronic device (1), comprising: One or more control circuits (2); And a memory device (3) storing one or more programs configured to be executed by the one or more control circuits (2), the one or more programs including instructions for performing the method (100) according to any one of claims 1 to 8.

11. A method (200) for determining bonds in a particle trajectory and predicting forces in the particle trajectory, comprising the following steps: - Obtain a dataset of particle trajectories in a (201) material system; - Dynamically identify the bonds between particles in the material system (202); - Determine (203) at least one bond graph based on the identified bonds in the material system; - Based on the partitioning of the at least one bond graph, characterize (204) at least one type of interaction of at least one particle in the at least one bond graph; - Provide (205) a predefined scheme including average force field data, which is data related to the force field acting on each characterized interaction type of particle.

12. The method of claim 11, further comprising the step of: The trajectory of the bonds identified in the material system over time (206) based on the predefined scheme.

13. The method (200) according to any one of claims 11 or 12, wherein, The step of dynamically identifying the bonds (202) between particles in the material system includes: - Select candidate bonds that include a pair of particles; - The candidate key is determined to be combined in the following cases: i. During a first predetermined time period (t1), based on the combination of particle radii (r1, r2) of the pair of particles (10, 11), the pair of particles (10, 11) is closer than a predetermined maximum distance; ii. During the second predetermined time period (t2), the average distance (d') between the pairs of particles (10, 11) is within a tolerance (t') associated with at least one of the following: the peak value of the partial radial distribution function pRDF of the pairs of particles (10, 11), or a measure of the nearest neighbor distance or equilibrium bond length of the pairs of particles (10, 11); and iii. During a third predetermined time period (t3), the first particle (10) of the candidate bond is not present in the repellent (15) associated with the second particle (11) and any other particle (12) in the candidate bond, or the first particle of the candidate bond satisfies the bond length criterion if it is present in the repellent (15).

14. The method (200) according to claim 11, wherein, The average force field data for each interaction type is obtained from the distribution of generalized forces on the generalized force field description coordinates, where each interaction type is associated with at least one generalized force field description coordinate.

15. The method (200) according to claim 11, wherein, The average force field data is at least one or any combination of the average value of the force distribution, the modal value of the force distribution, or the median value of the force distribution.

16. The method (200) according to claim 12, wherein, The propagation (206) includes: performing time integration on the material system from a first time point to a second time point.

17. The method (200) according to claim 14, wherein, The interaction type is at least one of two-body bonded or non-bonded interaction, three-body bonded or non-bonded interaction, four-body bonded or non-bonded interaction, and n-body bonded or non-bonded interaction, where n is any non-negative integer.

18. The method (200) according to claim 11, further comprising the step of: Use (205') force field data to generate a smooth function that depends on at least one generalized force field description coordinate.

19. A computer-readable storage medium storing one or more programs configured to be executed by one or more control circuits of an electronic device, said one or more programs comprising instructions for performing the method (200) according to any one of claims 11 to 18.

20. An electronic device (1), comprising: One or more control circuits (2); And a memory device (3) storing one or more programs configured to be executed by the one or more control circuits (2), the one or more programs including instructions for executing the method (200) according to any one of claims 11 to 18.

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