Denoising diffusion model for coarseness molecular dynamics

Abstract

A computing system includes a processor configured to receive atomic molecular dynamics simulation data for a plurality of training-time conformations of an atomic structure of a molecule. The processor is further configured to calculate coarseness molecular dynamics simulation data for the molecule based at least in part on the atomic molecular dynamics simulation data. The coarseness molecular dynamics simulation data is calculated at least in part by converting an atomic structure into a coarseness structure of a molecule. The processor is further configured to train a de-noising diffusion model using the coarseness molecular dynamics simulation data. At the de-noising diffusion model, the processor is further configured to receive a runtime conformation of the coarse-grained structure; and generating a coarseness force field estimate associated with the runtime conformation. The processor is further configured to output the coarseness force field estimate to the molecular dynamics simulation module; and generating, at a molecular dynamics simulation module, a molecular dynamics simulation of the molecule based at least in part on the coarseness force field estimate.

Description

Background Art

[0001] Coarse-grained (CG) molecular dynamics (MD) promises to extend the simulation of molecules to much larger spatial and temporal scales than currently achievable through atomistic MD simulations. Scaling up MD by orders of magnitude will enable new studies of macromolecular dynamics over much longer timescales, such as large protein folding events and slow interactions between macromolecules. CG MD enables the study of biological processes at temporal and spatial scales that are intractable at atomic resolution. For example, CG MD simulations are sometimes used in pharmaceutical research.

[0002] To obtain a CG simulation model, an all-atom or fine-grained representation is first mapped to a coarse-grained representation, for example, by grouping certain atoms together to form CG beads. Secondly, a CG force field is calculated. By using the CG force field acting on the CG beads, a CG molecular dynamics simulation reproduces the relevant features of the molecular system. In a top-down approach, a CG model is defined as reproducing the ensemble average of specific observables, which are experimentally measured and / or simulated on the fine-grained model. In a bottom-up approach, the CG model reproduces the behavior (e.g., thermodynamics or kinetics) of the fine-grained model. In the latter case, a previous approach is to define a CG force field for a chosen CG representation by enforcing thermodynamic consistency. When using this approach, simulations following the CG model have equilibrium distributions that are roughly the same as those obtained by projecting an equilibrium all-atom simulation onto the CG resolution. Summary of the Invention

[0003] According to one aspect of the present disclosure, a computing system is provided, comprising a processor configured to receive atomic molecular dynamics simulation data of multiple training conformations of the atomic structure of a molecule. The processor is also configured to calculate coarse-grained molecular dynamics simulation data of the molecule based at least in part on the atomic molecular dynamics simulation data. The coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into the coarse-grained structure of the molecule. The processor is also configured to train a denoised diffusion model using the coarse-grained molecular dynamics simulation data. At the denoised diffusion model, the processor is also configured to receive a runtime conformation of the coarse-grained structure. The processor is also configured to generate a coarse-grained force field estimate associated with the runtime conformation. The processor is also configured to output the coarse-grained force field estimate to a molecular dynamics simulation module. The processor is also configured to generate a molecular dynamics simulation of the molecule at the molecular dynamics simulation module based at least in part on the coarse-grained force field estimate.

[0004] This Summary is provided to introduce a selection of concepts that are further described below in a simplified form in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to implementations that solve any or all disadvantages noted in any part of this disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Figure 1 A computing system is schematically illustrated when training data for a denoising diffusion model is generated according to an example embodiment.

[0006] Figure 2 Shown according to Figure 1 Examples of atomic and coarse-grained structures are provided for the example of an alanine dipeptide and a rapidly folding protein.

[0007] Figure 3 Schematically shows the Figure 1 Example of a computational system during training of a denoising diffusion model.

[0008] Figure 4 Schematically shows the Figure 1 The computing system of an example during runtime when the processor is configured to generate a coarse-grained force field estimate at a denoised diffusion model.

[0009] Figure 5 Schematically shows the Figure 1 The computing system of an example of an example wherein the processor is further configured to generate a plurality of independent and identically distributed samples at the denoised diffusion model.

[0010] Figure 6 Shown according to Figure 1 Plot of the Jensen-Shannon divergence between the joint distribution of dihedral angles in a coarse-grained representation of an alanine dipeptide when the coarse-grained representation is modeled using different techniques.

[0011] Figure 7A Shown according to Figure 1 A flowchart of an example method for a computing system to perform training and inference on a denoised diffusion model used in molecular dynamics simulations.

[0012] Figure 7B shows what can be performed in some examples when training a denoising diffusion model Figure 7A Additional steps of the method.

[0013] Figure 7C shows that it is possible to perform calculations on coarse-grained molecular dynamics simulation data. Figure 7AAdditional steps of the method.

[0014] Figure 7D shows that a method can be performed to generate independent and identically distributed samples from a balanced distribution of coarse-grained structures. Figure 7A Additional steps of the method.

[0015] Figure 8 Shows that you can instantiate Figure 1 Schematic diagram of an example computing environment for a computing system. DETAILED DESCRIPTION

[0016] Traditional bottom-up coarse-graining techniques that rely on thermodynamic consistency principles have produced remarkable results over the past decade, especially when combined with machine learning methods. Two of these bottom-up coarse-graining techniques are variational force matching and relative entropy minimization, as discussed in further detail below. Variational force matching minimizes the mean squared error between the model's CG forces and the atomic forces projected onto the CG space. However, due to the stochastic nature of the projected forces, this noisy force matching estimator has large variance, resulting in inefficient data training. Variational force matching methods also require storing the values ​​of the atomic forces.

[0017] Alternatively, relative entropy minimization methods perform density estimation in CG space without access to atomic forces. Relative entropy minimization methods are often equivalent to energy-based models. Since training these models requires iteratively sampling from the model to estimate the log-likelihood gradient, relative entropy minimization methods require much higher computational cost than variational force matching methods.

[0018] Flow matching methods have also been recently introduced to alleviate the shortcomings of variational force matching methods and relative entropy minimization methods, such as sample inefficiency and the need to store atomic force values. In the first density matching stage performed during flow matching, the CG density is modeled with an enhanced normalized flow. In a second learning stage with a similar force matching goal, a deterministic CG force field is extracted. The deterministic CG force field can then be used in CG molecular dynamics simulations. Flow matching improves the performance of some rapidly folding proteins. However, the learned CG models are sometimes quantitatively inaccurate in reproducing the thermodynamics of the corresponding fine-grained model, and extension to larger proteins can lead to instabilities.

[0019] In the systems and methods discussed below, denoised diffusion is used to train a generative model on an equilibrium sample of CG structures. Training the generative model with a denoising loss function and a conservative score function produces a single model that can be used to generate independent and identically distributed (iid) CG samples and estimate the CG force field for CG molecular dynamics simulations. The denoised diffusion model can be trained in a single-stage training setup that is simpler than the training setup used in other machine learning-based CG molecular simulation methods. Additionally, the denoised diffusion model may have improved performance in several small to medium-sized protein simulations, thereby reproducing the CG equilibrium distribution and preserving the dynamics of all-atom simulations (such as protein folding events). The denoised diffusion model also allows for expansion to larger protein sizes than flow matching methods.

[0020] Figure 1 The computing system 10 is schematically shown when training data for the denoising diffusion model 40 is generated. Figure 1 The computing system 10 shown includes a processor 12 and a memory 14. The processor 12 includes one or more processing devices, such as one or more central processing units (CPUs), graphics processing units (GPUs), dedicated hardware accelerators, or other processing devices. The memory 14 includes one or more memory devices, which can be volatile memory devices and / or non-volatile memory devices.

[0021] In some examples, the components of computing system 10 may be provided within a single computing device. Alternatively, the components of computing system 10 may be distributed across multiple physical computing devices, such as multiple server computing devices located in a data center. In examples where computing system 10 includes a server computing device, the server device may be configured to communicate with a client computing device, such as to receive user input and output the results of a requested computation to a user of the client computing device.

[0022] like Figure 1 As shown, a denoised diffusion model 40 is trained to simulate a molecule. A molecule can be defined using an atomic structure 20, which indicates a plurality of atoms 21 included in the molecule. The atomic structure 20 also indicates a plurality of bonds 22 between the atoms 21. Thus, the atomic structure 20 can be a graphical representation of a molecule.

[0023] The processor 12 is further configured to receive atomic molecular dynamics simulation data 24. The atomic molecular dynamics simulation data 24 is generated by simulating a plurality of training conformations 28 of the atomic structure 20 of the molecule. In the atomic molecular dynamics simulation data 24, the training conformations are associated with a corresponding plurality of training simulation time steps 26. In some examples, such as Figure 1As shown, processor 12 is configured to sample a plurality of training conformations 28 from the atomic Boltzmann distribution 23 of the atomic structure 20, as discussed in further detail below.

[0024] Processor 12 is further configured to convert the atomic structure 20 into a CG structure 30 of the molecule. Processor 12 is configured to generate the CG structure 30 at least in part by reducing the dimension of the atomic structure 20. The CG structure 30 includes a plurality of CG beads 31 coupled by a plurality of CG bonds 32, where each CG bead 31 in the CG beads 31 includes one or more atoms 21 included in the atomic structure 20. Accordingly, when generating the CG structure 30, groups of atoms 21 are represented as CG beads 31 in a combined manner.

[0025] The calculation of the CG structure 30 can utilize a coarse-graining mapping that transforms a high-dimensional atomic representation into a lower-dimensional CG representation to describe, where n << N. For a molecular system, the CG mapping Ξ is typically linear, such that and returns the Cartesian coordinates z of the CG beads 31 as a linear combination of the Cartesian coordinates x of the set of representative atoms 21.

[0026] Figure 2 Shows examples of the atomic structure 20 (also referred to as the fine-grained structure) and the CG structure 30 for alanine dipeptide and for the fast-folding proteins chignolin, Trp-cage, Bba, villin, and protein G. In Figure 2 the example, the CG structure 30A generated from the atomic structure 20A of alanine dipeptide includes five CG beads, which are represented as nodes of a chain structure in Figure 2 the example. The CG structure 30B generated from the atomic structure 20B of chignolin includes 10 CG beads; the CG structure 30C generated from the atomic structure 20C of Trp-cage includes 20 CG beads; the CG structure 30D generated from the atomic structure 20D of Bba includes 28 CG beads; the CG structure 30E generated from the atomic structure 20E of villin includes 35 CG beads; the CG structure 30F generated from the atomic structure 20F of protein G includes 56 CG beads. These proteins can be coarse-grained by cutting out the atoms C for each amino acid α to produce one bead per residue.

[0027] Return Figure 1In the example of , the processor 12 is further configured to calculate CG molecular dynamics simulation data 34 of the molecule based at least in part on the atomic molecular dynamics simulation data 24 and the CG structure 30. The CG molecular dynamics simulation data 34 may include a plurality of training-time CG conformations 36 respectively associated with a plurality of training simulation time steps 26 used in the atomic molecular dynamics simulation data 24. Calculating the CG molecular dynamics simulation data 34 may include mapping the plurality of training-time conformations 28 onto the CG structure 30 to obtain a plurality of training-time CG conformations 36 included in the CG molecular dynamics simulation data 34. Accordingly, the training-time CG conformations 36 may be samples from the CG Boltzmann distribution 33.

[0028] The processor 12 is further configured to train the denoised diffusion model 40 using the CG molecular dynamics simulation data 34. Converting the atomistic molecular dynamics simulation data 24 to CG molecular dynamics simulation data 34 before training the denoised diffusion model 40 can improve the efficiency of training by compressing the atomistic molecular dynamics simulation data 24 into a form that can be learned more quickly.

[0029] The calculation of the force field data at the denoised diffusion model 40 is discussed below. As described above, the atomic molecular dynamics simulation data 24 can be sampled from the atomic Boltzmann distribution 23. The atomic structure 20 at a specific temperature The probability density under is given by the Boltzmann distribution Description, where U(x) is the potential energy of the system and k B is the Boltzmann constant.

[0030] In some examples, processor 12 may also be configured to compute a CG Boltzmann distribution 33 based at least in part on atomic Boltzmann distribution 23. By identifying a set of atomic configurations x that map to CG configuration z, the probability density of CG configuration z may be explicitly expressed as the following CG Boltzmann distribution 33: where δ(·) is the Dirac delta function. Without considering the additive constant, the above distribution uniquely defines the effective CG potential energy with a thermodynamically consistent mean force V(z). The mean force V(z) is given by:

[0031] In related molecular systems, the integral in the above equation is intractable. Therefore, methods have been proposed to approximate the thermodynamically consistent effective CG potential. Variational force matching is an existing method to approximate the effective CG potential. Under certain constraints applied to the CG map Ξ, a coarse-grained force field can be obtained. and atomic force fields When the CG map Ξ is a linear map, and when each CG bead 31 has at least one atom with a non-zero coefficient only for that particular CG bead 31, the following relationship holds: where Ξ f is a linear map whose coefficients are related to the linear coefficients of the CG map Ξ. The above equations for the CG force field can be used to approximate the thermodynamically consistent CG potential V by finding parameter values ​​that minimize the following variational loss θ (z) (expressed as a function of a set with parameter θ):

[0032] Another existing approach to obtain CG forces is via relative entropy minimization, where optimizing the density implicitly leads to an optimized mean potential function. Specifically, the CG density is estimated by minimizing the relative entropy, which is expressed as the Kullback-Leibler divergence where p θ (z) is the learned CG density function. Solving the above minimization problem is equivalent to optimizing the maximum likelihood when a finite number of samples are drawn from p(z). This can be done using the relationship From the optimized model density p θ (z). Unlike variational force matching, relative entropy minimization does not impose any constraints on the CG map Ξ, and no atomic forces are required for training.

[0033] Typically, the average potential energy V is directly parameterized by θ To learn the CG density function p θ The unnormalized version of is modeled, resulting in the relationship To minimize the relative entropy, the free energy of the model (normalization constant) can be estimated. Alternatively, iid samples can be extracted from the model and used to perform gradient estimation. However, both methods are impractical for high-dimensional problems.

[0034] As an alternative to variational force matching and relative entropy maximization, explicit density models in the form of normalized flows have been used in some existing CG force calculation methods. In principle, the standard normalized flow has a tractable normalized density p θ(z), thereby allowing direct maximum likelihood density estimation and force field learning. However, expressive reversible functions are difficult to learn. Instead, an auxiliary normalized flow can be used to model the flow density. The introduction of auxiliary random variables increases the expressiveness of the flow at the cost of intractable marginal likelihood, resulting in a minimization objective that is a variational upper bound on the relative entropy. Additionally, stochastic estimates of the CG forces can be extracted from the auxiliary normalized flow model alone. In order to extract a deterministic approximate mean force to simulate CG dynamics, a teacher-student setup can be used. This two-stage approach is called flow matching.

[0035] As mentioned above, this paper provides a denoised diffusion model 40 for coarse-grained molecular dynamics as an alternative to the conventional CG force modeling techniques mentioned above. The denoised diffusion probability model (DDPM) samples from a probability distribution by approximating the inverse process of the diffusion process (denoising process). The diffusion (forward) process is defined as an L-step Markov chain (Markov chain) where z0 is a sample from the unknown data distribution q(z0). The learned reverse process is defined as L ) is a reverse time Markov chain of L denoising steps starting from . The denoising step is expressed as:

[0036] For real-valued random variables, the distribution for the forward process can be a Gaussian distribution such that In this equation, {β i} is a fixed variance parameter that increases with i, making the Markov chain have a standard normal stationary distribution. The inverse process distribution can have the same functional form:

[0037] In the above equation, μ θ (z i ,i) is the mean of the Gaussian distribution, expressed as a learnable function with parameter θ. is a fixed variance.

[0038] Figure 3 The computing system 10 is schematically shown in more detail during training of the denoising diffusion model 40. Figure 3In the example of FIG, during a plurality of diffusion iterations 50 performed when training the denoised diffusion model, the processor 12 is configured to calculate a corresponding plurality of updated sets 56 of coordinate vectors associated with the CG beads 31. The processor 12 can be configured to perform L diffusion iterations 50 starting from the training-time CG conformation 36. Additionally, the processor 12 can be configured to perform each of the diffusion iterations 50 at least in part by sampling the updated set 56 of coordinate vectors from a corresponding Gaussian distribution 54. The Gaussian distribution 54 for the i-th diffusion iteration 50 can be calculated using the equation q(z) discussed above. i |z i-1 The set 56 of updated coordinate vectors calculated at each diffusion iteration in the diffusion iterations 50 comprises the coordinates of the CG beads 31 after diffusion has been applied to the CG structure 30. When performing training, closed-form marginalization of the Gaussian distribution 54 may be used.

[0039] Additionally, during each of the diffusion iterations 50, the processor 12 may be further configured to calculate a mean 58 of the Gaussian distribution 54 at least in part by executing the noise prediction neural network 44. The mean 58 of the Gaussian distribution 54 for each of the diffusion iterations 50 may be parameterized as follows: where ∈ θ (z i ,i) is the noise prediction neural network 44. In the above equation, α i =1-β i and The noise prediction neural network 44 may be, for example, a graph transformer network.

[0040] During the training of the denoised diffusion model 40, after each diffusion iteration of the diffusion iterations 50, the processor 12 may also be configured to perform a denoising iteration 64. In each of the denoising iterations 64, the processor 12 may be configured to calculate a denoised distribution 66 (indicated above as p(z 0:L )) Accordingly, the denoising diffusion model 40 is configured to learn the inverse process of the diffusion process.

[0041] The processor 12 is also configured to calculate a loss value 62 at a loss function 60 when training the denoising diffusion model 40. The mean 58 may be used to parameterize the Gaussian distribution included in the loss function 62. The loss function 60 used during training is given by:

[0042] In the above expression for the loss function 60, q(z0) is the data distribution. Without considering the constant, when When , the above expression for the loss function 60 is a negative evidence lower bound.

[0043] In some examples, a K i = 1. With K i The DDPM loss with ∑ i = 1 is equivalent to the following weighted sum of the denoising score matching targets:

[0044] In the above expression for the sum of denoising score matching targets, and s θ (z i ,i) represents the score model. The equivalence of the loss function 60 with the weighted sum of the denoising score matching objectives is obtained by substituting the score model s θ (z i ,i) and noise prediction network∈ θ (z i ,i) It is realized by the following association

[0045] Figure 4 The computing system 10 is schematically illustrated during runtime when the processor 12 is configured to generate a CG force field estimate 42 at the denoised diffusion model 40. The CG force field estimate 42 is generated after receiving a runtime conformation 70 of the CG structure 30. Additionally, according to Figure 4 In the example of , the processor 12 is further configured to output the CG force field estimate 42 to the molecular dynamics simulation module 80 .

[0046] At the molecular dynamics simulation module 80, the processor 12 is further configured to generate a molecular dynamics simulation 86 of the molecule based at least in part on the CG force field estimate 42. The molecular dynamics simulation 86 may be generated at least in part by executing a numerical solver 84 included in the molecular dynamics simulation module 80. The molecular dynamics simulation 86 may be a simulation of the movement of the CG beads 31 over time. The processor 12 may also be configured to output the molecular dynamics simulation 86 to an additional computational process 88, such as a graphical user interface (GUI) generation process or a biological interaction simulation program.

[0047] Given a sufficiently expressive model and sufficient data, the best score Approximate matching score where q(z i )=∫dz0q(z i|z0)q(z0) is the marginal distribution of the forward diffusion process at level i. Under sufficiently low noise levels, the marginal distribution q(z i ) is similar to the data distribution q(z0), such that Efficiently approximate the score of the unknown data distribution. When the unknown data distribution is equal to the CG Boltzmann distribution33, the optimal score at level i=1 This approximately matches the CG force:

[0048] Using scoring models θ (z i ,i) and noise prediction network∈ θ (z i ,i), the approximate CG force can be extracted from the denoised diffusion model as follows:

[0049] This CG force field estimate 42 is called a denoised force field.

[0050] While in principle the lowest level (i=1) is expected to provide the most accurate CG force field estimate 42, i may alternatively be considered a hyperparameter. In such an example, the value of i that produces the lowest loss value 62 during training may be selected by cross-validating the simulated dynamics of the CG structure 30.

[0051] At the molecular dynamics simulation module 80, the processor 12 may be configured to generate a molecular dynamics simulation 86 at least in part by approximating a solution to the Langevin equation 82 including the CG force field estimate 42. The CG molecular dynamics simulation 86 can be calculated by propagating the following Langevin equation 82 at the numerical solver 84:

[0052] In the Langevin equation 82 shown above, the substitution Additionally, M is a diagonal matrix M=diag(m1, . . . , m n ), γ is the friction coefficient, and w(t) is the average value The stationary Gaussian process of Δ(delta) The constants in the Langevin equation 82 can be set to the values ​​of those constants used when generating the atomic molecular dynamics simulation data 24. Thus, given a trained noise prediction network ∈ θ In such an example, the only remaining hyperparameter to tune is the noise level i.

[0053] In one limit of the Langevin equation, the masses m1,…,m n can be neglected, and the friction coefficient γ is large (with finite η = γM). This limit is known as Brownian dynamics or overdamped Langevin dynamics. Iteratively diffusing and denoising at the first noise level (i = 1) of the denoised diffusion model for one step is equivalent to running a Brownian dynamics or overdamped Langevin dynamics simulation with a time step of given.

[0054] The noise prediction neural network 44 is now discussed in more detail. The noise prediction neural network ∈ is selected based on the physical symmetry of the CG structure 30. θ One such symmetry is that the CG force field estimate 52 is conservative, i.e., it is equal to the CG energy potential V θ (z). Therefore, the noise prediction neural network ∈ θ (z i ,i) Gradient of a neural network parameterized with scalar output: in The score used in the expression for the loss function 60 is parameterized as the gradient of an energy function. Using a conservative score function at the denoised diffusion model 40 allows for the computation of stable molecular dynamics simulations 86 using the extracted CG force field estimate 42.

[0055] The noise prediction neural network 44 also exhibits translation invariance and rotation invariance. Translation invariance satisfies ∈ θ (z)=∈ θ (z+t) This symmetry can be imposed by inputting the coordinates of the CG beads 31 into the noise prediction neural network 44 in the form of a plurality of pairwise difference vectors 72 when specifying a runtime conformation 70. Each vector in the pairwise difference vectors 72 can be of the form z (i) -z (j) , where i and j are indices of the CG beads 31. Thus, the pairwise difference vectors 72 can indicate the distances between the CG beads 31 in the runtime conformation 70. The noise prediction neural network 44 can, for example, be a two-layer graph transformer adapted to the above-mentioned symmetry constraints. Since the noise prediction neural network 44 is translation-invariant and rotation-equivariant, the CG force field estimate 52 can also be translation-invariant and rotation-equivariant.

[0056] Figure 5 The computing system 10 in the example is schematically shown, wherein the processor 12 is further configured to generate a plurality of independent and identically distributed (iid) samples 90 at the denoised diffusion model 40. The iid samples 90 may be sampled from an equilibrium distribution of the CG structure 30, which is Figure 5Such iid samples 90 can be calculated without explicitly generating the CG Boltzmann distribution 33. Figure 1 and Figure 3 As discussed, the CG molecular dynamics simulation data 34 used to train the denoised diffusion model 40 can be derived from the CG Boltzmann distribution Using the trained denoising diffusion model 40 parameterized by the noise prediction neural network 44, the iid samples of the approximate CG equilibrium distribution can be obtained by Generate by ancestral sampling.

[0057] The processor 12 may also be configured to output the plurality of iid samples 90 to the molecular dynamics simulation module 80 . At the molecular dynamics simulation module 80 , the processor 12 may also be configured to generate a molecular dynamics simulation 86 of the molecule based at least in part on the plurality of iid samples 90 .

[0058] The following discusses Figure 2 Example experimental results for simulations of alanine dipeptide and rapidly folding proteins are shown. In these experimental results, the denoised diffusion model 40 (referred to as DFF(sim.) and DFF(iid) when used for force field estimation and iid sample generation, respectively) is compared with three different baselines: CGNet sim., Flow iid, and Flow-CGNet sim. CGNet sim. is a pure force matching neural network trained on CG forces sliced ​​from a fine-grained representation. Flow iid is a force-independent normalized flow trained on CG molecular dynamics simulation data 34. Flow-CGNet sim. is a force field obtained by training a force matching neural network (CGNet, “student”) on the gradient of the flow model (“teacher”) using a teacher-student setup. The denoised diffusion model 40 discussed above does not require a teacher-student setup because the symmetry constraints are already integrated into the network of the denoised diffusion model 40. Therefore, the denoised diffusion model 40 can be used as a force field simulator and iid sampler without further training. The results obtained from each of the above models can be compared with real reference data obtained from fine-grained molecular dynamics simulations.

[0059] The denoised diffusion model 40 was first evaluated on the CG structure 30A of the alanine dipeptide for all-atom simulations. Figure 2As shown, the CG structure 30A is cleaved from the five central backbone atoms of the molecule into CG beads 31. CG molecular dynamics simulation data 34 were generated in four independent runs, each with a simulation time of 500 ns and 250,000 sample points saved per simulation (2 ps interval). The model was evaluated in a four-fold cross-validation setting, with three simulations used for training and validation and one simulation used for testing.

[0060] In the Langevin dynamics simulation of the alanine dipeptide molecule, the system was simulated for 1 million iterations with a time step resolution of 2 femtoseconds. A sample was saved every 250 iterations, resulting in 4K samples per simulation. 100 simulations were run in parallel, resulting in a total of 400,000 samples. The mass of each coarse-grained node was set to 12.8 g / mol, which is the weighted average of the masses of the carbon and oxygen atoms in the molecule. The temperature and friction coefficient were set to 300 K and 1 ps, respectively. -1 .

[0061] The noise prediction neural network 44 for alanine dipeptide simulation is a 2-layer graph transformer with 96 hidden features in each layer. The neural network is 3·10 -4 The learning rate is trained, and the cosine learning rate is decayed to 1·10 -5 The denoising diffusion model 40 was evaluated after training on the following number of training data: {10K, 20K, 50K, 100K, 200K, 500K}. The batch size was 1024. Early stopping was performed for the training set sizes 10K and 20K. The following values ​​of the noise level i for different numbers of samples were obtained via cross-validation: Training samples 10K 20K 50K 100K 200K 500K Noise level i 26 25 20 19 17 8

[0062] In the alanine dipeptide simulation, two dihedral angles φ and ψ were calculated along the coarse-grained backbone of the alanine dipeptide molecule. These two angles are controlled by the four-body interactions that describe the main degrees of freedom of the CG structure 30A. Figure 6 A plot 100 of the Jensen-Shannon (JS) divergence between the joint distribution of dihedral angles φ and ψ in the training set and validation partitions when modeling the CG structure 30A using different techniques is shown. The JS divergence is shown for different neural networks CGNet(sim.), Flow-CGNet(sim.), Flow(iid), Reference, DFF(sim.), and DFF(iid) after each being trained with 500K samples.

[0063] like Figure 6As shown, DFF sim. outperforms previous CG simulation methods (Flow-CGNetsim. and CGNet sim.) across all tested data ranges. In low-data settings, DFF is more data-efficient than previous methods in both iid and simulation settings. DFF sim. also outperforms previous models over a wider range of data, closely matching the lower bound of the JS divergence.

[0064] Experiments were also performed in which the corresponding denoised diffusion model 40 was trained using the above denoised force field technique on five rapidly folding proteins: chignolin, tryptophan cage, Bba, villin, and protein G. As described above, the fine-grained and coarse-grained structures of these proteins are shown in Figure 2 The simulation length varied, but for each trajectory, the frames were randomly shuffled and split into training, validation, and test sets with a 70%-10%-20% split. For each protein, the interval between frames was 200 picoseconds. During the denoising diffusion process, a cosine scheduler with 1000 different noise levels i was used.

[0065] The following table shows additional details related to the training of the denoised diffusion model 40 for proteins:

[0066] The following table shows the hyperparameters used at denoising diffusion model 40 in the protein modeling experiments:

[0067] In the Langevin dynamics simulations, 6 million simulation steps were performed, with samples saved every 500 steps. 100 simulations were run in parallel, generating 1.2 million samples. The particle mass was set to 12 g / mol. The temperature used in the Langevin dynamics simulations was the same as that used in the real data.

[0068] The following table shows the JS divergence of the time-delayed independent component (TIC) distribution and the pairwise distance (PWD) distribution for each rapidly folding protein. In the table below, the denoised diffusion model is compared with Flow for the iid sample generation task and with Flow-CGNet for the force field simulation task.

[0069] As shown in the table above, DFF(iid) and DFF(sim.) outperform the baseline methods Flow(iid) and Flow-CGNet(sim.) on the balance metrics TIC JS and PWD JS.

[0070] Figure 7A A flow chart of a method 200 for a computing system to perform training and inference on a denoised diffusion model used in a molecular dynamics simulation is shown. At step 202, method 200 includes receiving atomistic molecular dynamics simulation data for a plurality of training conformations of an atomic structure of a molecule. The training conformations can be associated with corresponding training simulation time steps. Accordingly, the atomistic molecular dynamics simulation data can include a set of training conformations that provide examples of movement trajectories of atoms included in the atomic structure over time.

[0071] At step 204, method 200 further includes calculating CG molecular dynamics simulation data for the molecule based at least in part on the atomic molecular dynamics simulation data. Step 204 may include, at step 206, converting the atomic structure into a coarse-grained structure of the molecule when calculating the coarse-grained molecular dynamics simulation data. Additionally, at step 208, generating the coarse-grained structure at step 206 may include reducing the dimensionality of the atomic structure. A coarse-grained mapping that projects atoms of the atomic structure onto a plurality of coarse-grained beads included in the CG structure may be used to reduce the dimensionality of the atomic structure.

[0072] At step 210, method 200 further includes training a denoised diffusion model using the coarse-grained molecular dynamics simulation data. The denoised diffusion model can be trained using a loss function that includes a term proportional to the gradient of the energy function. The loss function can result in a denoised diffusion network that models the conservative forces exerted by the molecules.

[0073] Steps 212 and 214 are performed at the denoised diffusion model during runtime. At step 212, method 200 also includes receiving a runtime conformation of the CG structure. At step 214, method 200 also includes generating a CG force field estimate associated with the runtime conformation. In some examples, the runtime conformation can be specified by a plurality of pairwise difference vectors indicating distances between CG beads. In such examples, the CG force field estimate can be translationally invariant and rotationally equivariant.

[0074] At step 216, method 200 further includes outputting the CG force field estimate to a molecular dynamics simulation module. At step 218, method 200 further includes generating a molecular dynamics simulation of the molecule at the molecular dynamics simulation module based at least in part on the CG force field estimate. For example, generating the molecular dynamics simulation may include numerically approximating the Langevin equation including the coarse-grained force field estimate. In such an example, the Langevin equation may be used to model the Brownian motion of the molecule.

[0075] Figure 7BAdditional steps of method 200 that may be performed in some examples when training a denoised diffusion model are shown. At step 220, during a plurality of diffusion iterations performed while training the denoised diffusion model, method 200 may also include calculating a corresponding set of multiple updated coordinate vectors associated with the coarse-grained beads. Step 220 may include, at step 222, sampling the set of updated coordinate vectors from a corresponding Gaussian distribution. Accordingly, during the diffusion phase of training, Gaussian noise may be applied to the training conformation.

[0076] Calculating the updated coordinate vector at step 220 may also include calculating a mean of a Gaussian distribution at least in part by executing a noise prediction neural network at step 224. In some examples, the noise prediction neural network may be a graph transformer network. The mean may be used to parameterize the Gaussian distribution from which the updated coordinate vector is sampled during the diffusion iteration.

[0077] At step 226, method 200 may further include calculating a plurality of denoised distributions during a corresponding plurality of denoising iterations. The denoised distributions may be calculated based at least in part on a Gaussian distribution and a set of updated coordinate vectors. The Gaussian distributions may be parameterized using the mean values ​​calculated in the diffusion iterations at step 224. During the denoising iterations, the denoising diffusion network may learn an inverse process of the diffusion process.

[0078] Figure 7C Additional steps of method 200 that may be performed when CG molecular dynamics simulation data is calculated at step 204 are shown. At step 228, method 200 may further include sampling a plurality of training conformations from an atomic Boltzmann distribution of the atomic structure. At step 230, method 200 may further include mapping the plurality of training conformations onto the coarse-grained structure to obtain a plurality of training coarse-grained conformations included in the coarse-grained molecular dynamics simulation data. Thus, the training conformations sampled from the atomic Boltzmann distribution can be converted to CG conformations sampled from the CG Boltzmann distribution.

[0079] Figure 7D Steps of method 200 are shown that can be additionally or alternatively performed to generate and output a CG force field estimate. At step 232, method 200 can also include generating a plurality of iid samples from an equilibrium distribution of coarse-grained structures at the denoised diffusion model. Method 200 can also include outputting the plurality of iid samples to a molecular dynamics simulation module at step 234. At step 236, method 200 can also include generating a molecular dynamics simulation of the molecule at the molecular dynamics simulation module based at least in part on the plurality of iid samples. Accordingly, the denoised diffusion network can be used to generate the iid samples as well as the force field estimate.

[0080] In some embodiments, the methods and processes described herein may be bound to a computing system of one or more computing devices. In particular, such methods and processes may be implemented as computer applications or services, application programming interfaces (APIs), libraries, and / or other computer program products.

[0081] Figure 3 A non-limiting embodiment of a computing system 300 is schematically shown that can perform one or more of the methods and processes described above. The computing system 300 is shown in simplified form. The computing system 300 can embody the above described and illustrated Figure 1 Components of computing system 300 may be instantiated in one or more personal computers, server computers, tablet computers, home entertainment computers, network computing devices, video gaming devices, mobile computing devices, mobile communication devices (e.g., smartphones), and / or other computing devices, as well as wearable computing devices (such as smartwatches and head-mounted augmented reality devices).

[0082] The computing system 300 includes a logic processor 302, a volatile memory 304, and a non-volatile storage device 306. The computing system 300 may optionally include a display subsystem 308, an input subsystem 310, a communication subsystem 312, and / or Figure 8 Other components not shown.

[0083] Logical processor 302 includes one or more physical devices configured to execute instructions. For example, a logical processor can be configured to execute instructions that are part of one or more applications, programs, routines, libraries, objects, components, data structures, or other logical constructs. Such instructions can be implemented to perform a task, implement a data type, transform the state of one or more components, achieve a technical effect, or otherwise achieve a desired result.

[0084] The logical processor may include one or more physical processors configured to execute software instructions. Additionally or alternatively, the logical processor may include one or more hardware logic circuits or firmware devices configured to execute hardware-implemented logic or firmware instructions. The processor of the logical processor 302 may be single-core or multi-core, and the instructions executed thereon may be configured for sequential, parallel and / or distributed processing. The individual components of the logical processor may optionally be distributed across two or more separate devices that may be remotely located and / or configured for coordinated processing. Various aspects of the logical processor may be virtualized and executed by a remotely accessible networked computing device configured in a cloud computing configuration. In this case, it will be understood that these virtualized aspects are run on different physical logical processors of various different machines.

[0085] The non-volatile storage device 306 includes one or more physical devices configured to hold instructions executable by a logical processor to implement the methods and processes described herein. When implementing such methods and processes, the state of the non-volatile storage device 306 may be transformed, for example, to hold different data.

[0086] The non-volatile storage device 306 may include a removable and / or built-in physical device. The non-volatile storage device 306 may include optical memory, semiconductor memory, and / or magnetic memory, or other mass storage device technologies. The non-volatile storage device 306 may include a non-volatile, dynamic, static, read / write, read-only, sequential access, location addressable, file addressable, and / or content addressable device. It should be understood that the non-volatile storage device 306 is configured to retain instructions even when the non-volatile storage device 306 is powered off.

[0087] Volatile memory 304 may include a physical device that includes random access memory. Volatile memory 304 is typically used by logical processor 302 to temporarily store information during the processing of software instructions. It should be understood that when volatile memory 304 is powered off, volatile memory 304 typically does not continue to store instructions.

[0088] Aspects of the logic processor 302, volatile memory 304, and non-volatile storage device 306 may be integrated together into one or more hardware logic components. For example, such hardware logic components may include field programmable gate arrays (FPGAs), program and application specific integrated circuits (PASIC / ASICs), program and application specific standard products (PSSP / ASSPs), systems on chips (SOCs), and complex programmable logic devices (CPLDs).

[0089] The terms "module," "program," and "engine" may be used to describe aspects of the computing system 300 that are typically implemented in software by a processor to use portions of volatile memory to perform a specific function, which involves transform processing that specifically configures the processor to perform the function. Thus, a module, program, or engine may be instantiated using portions of volatile memory 304 via a logical processor 302 executing instructions held by non-volatile storage device 306. It should be understood that different modules, programs, and / or engines may be instantiated from the same application, service, code block, object, library, routine, API, function, etc. Likewise, the same module, program, and / or engine may be instantiated by different applications, services, code blocks, objects, routines, APIs, functions, etc. The terms "module," "program," and "engine" may encompass individual or groups of executable files, data files, libraries, drivers, scripts, database records, and the like.

[0090] When the display subsystem 308 is included, the display subsystem 308 can be used to present a visual representation of the data held by the non-volatile storage device 306. The visual representation can take the form of a graphical user interface (GUI). Since the methods and processes described herein change the data held by the non-volatile storage device and thus transform the state of the non-volatile storage device, the state of the display subsystem 308 can also be transformed to visually represent the changes in the underlying data. The display subsystem 308 can include one or more display devices utilizing almost any type of technology. Such a display device can be combined with the logical processor 302, the volatile memory 304, and / or the non-volatile storage device 306 in a shared housing, or such a display device can be a peripheral display device.

[0091] When the input subsystem 310 is included, the input subsystem 310 may include or interface with one or more user input devices, such as a keyboard, mouse, touch screen, or game controller. In some embodiments, the input subsystem may include or interface with selected natural user input (NUI) components. Such components may be integrated or peripheral, and the conversion and / or processing of input actions may be handled internally or externally to the device. Example NUI components may include microphones for speech and / or voice recognition; infrared, color, stereo, and / or depth cameras for machine vision and / or gesture recognition; head trackers, eye trackers, accelerometers, and / or gyroscopes for motion detection and / or intent recognition; and electric field sensing components for assessing brain activity; and / or any other suitable sensors.

[0092] When included, the communication subsystem 312 can be configured to communicatively couple the various computing devices described herein to each other and to other devices. The communication subsystem 312 can include wired and / or wireless communication devices compatible with one or more different communication protocols. As non-limiting examples, the communication subsystem can be configured to communicate via a wireless telephone network or a wired or wireless local area network or wide area network. In some embodiments, the communication subsystem can allow the computing system 300 to send messages to and / or receive messages from other devices via a network such as the Internet.

[0093] The following paragraphs discuss several aspects of the present disclosure. According to one aspect of the present disclosure, a computing system is provided, comprising a processor configured to receive atomic molecular dynamics simulation data of multiple training conformations of an atomic structure of a molecule. The processor is further configured to calculate coarse-grained molecular dynamics simulation data of the molecule based at least in part on the atomic molecular dynamics simulation data. The coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into a coarse-grained structure of the molecule. The processor is further configured to train a denoised diffusion model using the coarse-grained molecular dynamics simulation data. At the denoised diffusion model, the processor is further configured to receive a runtime conformation of the coarse-grained structure; and generate a coarse-grained force field estimate associated with the runtime conformation. The processor is further configured to output the coarse-grained force field estimate to a molecular dynamics simulation module. The processor is further configured to generate a molecular dynamics simulation of the molecule at the molecular dynamics simulation module based at least in part on the coarse-grained force field estimate. The above features can have the technical effect of accurately simulating molecular dynamics in a manner that is more easily scalable to larger molecular sizes than previous methods.

[0094] According to this aspect, the processor may be configured to generate the coarse-grained structure at least in part by reducing the dimensionality of the atomic structure.The above features may have the technical effect of reducing the number of variables estimated by the denoised diffusion model, thereby allowing for more efficient training and inference.

[0095] According to this aspect, the coarse-grained structure may comprise a plurality of coarse-grained beads.The above features may have the technical effect of reducing the dimensionality of the atomic structure by grouping together sets of atoms that move together.

[0096] According to this aspect, during a plurality of diffusion iterations performed when training the denoised diffusion model, the processor can be configured to calculate a corresponding set of a plurality of updated coordinate vectors associated with the coarse-grained beads. The above-described feature can have the technical effect of applying noise to the coordinate vectors of the coarse-grained beads during the diffusion phase of training.

[0097] According to this aspect, the processor can be configured to perform each of the diffusion iterations at least in part by sampling a set of updated coordinate vectors from a corresponding Gaussian distribution.The above features can have the technical effect of randomly or pseudo-randomly generating noise applied to the coordinate vectors during the diffusion phase.

[0098] According to this aspect, during each of the diffusion iterations, the processor may be further configured to calculate a mean of the Gaussian distribution at least in part by executing a noise prediction neural network. The above features may have a technical effect of determining an amount of noise applied to a coordinate vector.

[0099] According to this aspect, the noise prediction neural network is a graph transformer network. The above features can have the technical effect of using a noise prediction neural network architecture that accurately and efficiently models the noise applied by the CG structure.

[0100] According to this aspect, the processor is configured to compute coarse-grained molecular dynamics simulation data at least in part by sampling a plurality of training conformations from an atomic Boltzmann distribution of the atomic structure. Computing the coarse-grained molecular dynamics simulation data may also include mapping the plurality of training conformations onto the coarse-grained structure to obtain the plurality of training coarse-grained conformations included in the coarse-grained molecular dynamics simulation data. This feature may have the technical effect of compressing the atomic molecular dynamics simulation data into a form that can be learned more quickly.

[0101] According to this aspect, at the molecular dynamics simulation module, the processor can be configured to generate a molecular dynamics simulation at least in part by approximately solving the Langevin equation including the coarse-grained force field estimate. The above features can have a technical effect of simulating the motion of molecules from the CG force field estimate.

[0102] According to this aspect, the coarse-grained force field estimate may be translationally invariant and rotationally equivariant.The above features may have the technical effect of reflecting the physical symmetries of the CG structure in the CG force field estimate.

[0103] According to this aspect, the runtime conformation may be specified by a plurality of pairwise difference vectors.The above features may have the technical effect of encoding translational invariance and rotational equivariance in the structure of the input data of the denoising diffusion model.

[0104] According to this aspect, the processor can also be configured to generate a plurality of independent and identically distributed (iid) samples from the equilibrium distribution of the coarse-grained structure at the denoised diffusion model. The processor can also be configured to output the plurality of iid samples to the molecular dynamics simulation module. The processor can also be configured to generate a molecular dynamics simulation of the molecule based at least in part on the plurality of iid samples. The above features can have the technical effect of generating iid samples of CG structures at the same machine learning model used to generate the CG force field estimate.

[0105] According to another aspect of the present disclosure, a method for a computing system is provided. The method includes receiving atomic molecular dynamics simulation data of multiple training conformations of the atomic structure of a molecule. The method also includes calculating coarse-grained molecular dynamics simulation data of the molecule based at least in part on the atomic molecular dynamics simulation data. The coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into a coarse-grained structure of the molecule. The method also includes training a denoised diffusion model using the coarse-grained molecular dynamics simulation data. At the denoised diffusion model, the method also includes receiving a runtime conformation of the coarse-grained structure and generating a coarse-grained force field estimate associated with the runtime conformation. The method also includes outputting the coarse-grained force field estimate to a molecular dynamics simulation module. The method also includes generating a molecular dynamics simulation of the molecule at the molecular dynamics simulation module based at least in part on the coarse-grained force field estimate. The above features can have the technical effect of accurately simulating molecular dynamics in a manner that is more easily scalable to larger molecular sizes than previous methods.

[0106] According to this aspect, generating the coarse-grained structure can include reducing the dimensionality of the atomic structure. The coarse-grained structure includes a plurality of coarse-grained beads. The above features can have the technical effect of reducing the number of variables estimated by the denoised diffusion model by grouping sets of atoms that move together, thereby allowing for more efficient training and inference.

[0107] According to this aspect, during a plurality of diffusion iterations performed when training the denoised diffusion model, the method may further include calculating a corresponding set of a plurality of updated coordinate vectors associated with the coarse-grained beads. The above feature may have the technical effect of applying noise to the coordinate vectors of the coarse-grained beads during the diffusion phase of training.

[0108] According to this aspect, performing each of the diffusion iterations may further include sampling a set of updated coordinate vectors from a corresponding Gaussian distribution. Performing each of the diffusion iterations may further include calculating a mean of the Gaussian distribution at least in part by executing a noise prediction neural network. The above features may have the technical effect of randomly or pseudo-randomly generating noise applied to the coordinate vectors during the diffusion phase. The above features may further have the technical effect of determining an amount of noise applied to the coordinate vectors.

[0109] According to this aspect, computing the coarse-grained molecular dynamics simulation data may include sampling a plurality of training conformations from an atomic Boltzmann distribution of the atomic structure. Computing the coarse-grained molecular dynamics simulation data may also include mapping the plurality of training conformations onto the coarse-grained structure to obtain the plurality of training coarse-grained conformations included in the coarse-grained molecular dynamics simulation data. This feature may have the technical effect of compressing the atomic molecular dynamics simulation data into a form that can be learned more quickly.

[0110] According to this aspect, the coarse-grained force field estimate may be translationally invariant and rotationally equivariant.The above features may have the technical effect of reflecting the physical symmetries of the CG structure in the CG force field estimate.

[0111] According to this aspect, the method may further include generating, at the denoised diffusion model, a plurality of independent and identically distributed (IID) samples from an equilibrium distribution of coarse-grained structures. The method may further include outputting the plurality of IID samples to a molecular dynamics simulation module. The method may further include generating a molecular dynamics simulation of a molecule based, at least in part, on the plurality of IID samples. The above features may have the technical effect of generating IID samples of CG structures at the same machine learning model used to generate the CG force field estimate.

[0112] According to another aspect of the present disclosure, a computing system is provided, comprising a processor configured to receive atomic molecular dynamics simulation data of multiple training conformations of the atomic structure of a molecule. The processor is also configured to calculate coarse-grained molecular dynamics simulation data of the molecule based at least in part on the atomic molecular dynamics simulation data. The coarse-grained molecular dynamics simulation data can be calculated at least in part by converting the atomic structure into the coarse-grained structure of the molecule. The processor is also configured to train a denoising diffusion model using the coarse-grained molecular dynamics simulation data. At the denoising diffusion model, the processor is also configured to generate multiple independent and identically distributed (iid) samples from the equilibrium distribution of the coarse-grained structure. The processor is also configured to output multiple iid samples. The above features can have the technical effect of efficiently performing training and inference at the denoising diffusion model to generate iid samples of the distribution of the conformation of the molecule.

[0113] As used herein, "and / or" is defined as inclusive or as specified by the following truth table: A B A∨B real real real real Fake real Fake real real Fake Fake Fake

[0114] It should be understood that the configurations and / or methods described herein are exemplary in nature, and these specific embodiments or examples should not be considered restrictive, as many variations are possible. The specific routines or methods described herein may represent one or more of any number of processing strategies. Therefore, the various actions shown and / or described may be performed in the order shown and / or described, in other orders, in parallel, or omitted. Likewise, the order of the above-described processes may be changed.

[0115] The subject matter of the present disclosure includes all novel and nonobvious combinations and subcombinations of the various processes, systems and configurations, and other features, functions, acts, and / or properties disclosed herein, as well as any and all equivalents thereof.

Claims

1. A computing system comprising: The processor is configured to: receiving atomic molecular dynamics simulation data of a plurality of training conformations of the atomic structure of the molecule; calculating coarse-grained molecular dynamics simulation data for the molecule based at least in part on the atomistic molecular dynamics simulation data, wherein the coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into a coarse-grained structure of the molecule; training a denoised diffusion model using the coarse-grained molecular dynamics simulation data; At the denoising diffusion model: receiving a runtime conformation of the coarse-grained structure; as well as generating a coarse-grained force field estimate associated with the runtime conformation; exporting the coarse-grained force field estimate to a molecular dynamics simulation module; as well as A molecular dynamics simulation of the molecule is generated at the molecular dynamics simulation module based at least in part on the coarse-grained force field estimate. 2 . The computing system of claim 1 , wherein the processor is configured to generate the coarse-grained structure at least in part by reducing the dimensionality of the atomic structure. The computing system of claim 2 , wherein the coarse-grained structure comprises a plurality of coarse-grained beads.

4. The computing system of claim 3, wherein during a plurality of diffusion iterations performed when training the denoised diffusion model, the processor is configured to compute a corresponding set of a plurality of updated coordinate vectors associated with the coarse-grained beads. 5 . The computing system of claim 4 , wherein the processor is configured to perform each of the diffusion iterations at least in part by sampling the set of updated coordinate vectors from a corresponding Gaussian distribution.

6. The computing system of claim 5, wherein during each of the diffusion iterations, the processor is further configured to calculate a mean of the Gaussian distribution at least in part by executing a noise prediction neural network.

7. The computing system of claim 6, wherein the noise prediction neural network is a graph transformer network.

8. The computing system of any one of claims 3 to 7, wherein the processor is configured to compute the coarse-grained molecular dynamics simulation data at least in part by: Sampling the plurality of training-time conformations from an atomic Boltzmann distribution of the atomic structure; and The multiple training conformations are mapped onto the coarse-grained structure to obtain multiple training coarse-grained conformations included in the coarse-grained molecular dynamics simulation data.

9. The computing system of any one of claims 1 to 8, wherein at the molecular dynamics simulation module, the processor is configured to generate the molecular dynamics simulation at least in part by approximately solving the Langevin equation including the coarse-grained force field estimate.

10. The computing system of any one of claims 1 to 9, wherein the coarse-grained force field estimate is translation-invariant and rotation-equivariant. The computing system of claim 10 , wherein the runtime conformation is specified by a plurality of pairwise difference vectors.

12. The computing system of any one of claims 1 to 11, wherein the processor is further configured to: generating, at the denoising diffusion model, a plurality of independent and identically distributed (iid) samples from an equilibrium distribution of the coarse-grained structure; Outputting the plurality of iid samples to the molecular dynamics simulation module; and The molecular dynamics simulation of the molecule is generated based at least in part on the plurality of iid samples.

13. A method for a computing system, the method comprising: receiving atomic molecular dynamics simulation data of a plurality of training conformations of the atomic structure of the molecule; calculating coarse-grained molecular dynamics simulation data for the molecule based at least in part on the atomistic molecular dynamics simulation data, wherein the coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into a coarse-grained structure of the molecule; training a denoised diffusion model using the coarse-grained molecular dynamics simulation data; At the denoising diffusion model: receiving a runtime conformation of the coarse-grained structure; as well as generating a coarse-grained force field estimate associated with the runtime conformation; exporting the coarse-grained force field estimate to a molecular dynamics simulation module; as well as A molecular dynamics simulation of the molecule is generated at the molecular dynamics simulation module based at least in part on the coarse-grained force field estimate.

14. The method according to claim 13, wherein: Generating the coarse-grained structure includes reducing the dimensionality of the atomic structure; and The coarse-grained structure includes a plurality of coarse-grained beads.

15. The method according to claim 14, further comprising: During a plurality of diffusion iterations performed when training the denoised diffusion model, a corresponding plurality of sets of updated coordinate vectors associated with the coarse-grained beads are calculated.

16. The method of claim 15, wherein performing each of the diffusion iterations further comprises: sampling the set of updated coordinate vectors from a corresponding Gaussian distribution; as well as The mean of the Gaussian distribution is calculated at least in part by executing a noise prediction neural network.

17. The method according to any one of claims 14 to 16, wherein calculating the coarse-grained molecular dynamics simulation data comprises: sampling the plurality of training-time conformations from an atomic Boltzmann distribution of the atomic structure; as well as The multiple training conformations are mapped onto the coarse-grained structure to obtain multiple training coarse-grained conformations included in the coarse-grained molecular dynamics simulation data.

18. A method according to any one of claims 13 to 17, wherein the coarse-grained force field estimate is translationally invariant and rotationally equivariant.

19. The method according to any one of claims 13 to 18, further comprising: generating, at the denoising diffusion model, a plurality of independent and identically distributed (iid) samples from an equilibrium distribution of the coarse-grained structure; Outputting the plurality of iid samples to the molecular dynamics simulation module; and The molecular dynamics simulation of the molecule is generated based at least in part on the plurality of iid samples.

20. A computing system comprising: The processor is configured to: receiving atomic molecular dynamics simulation data of a plurality of training conformations of the atomic structure of the molecule; calculating coarse-grained molecular dynamics simulation data for the molecule based at least in part on the atomistic molecular dynamics simulation data, wherein the coarse-grained molecular dynamics simulation data is calculated at least in part by converting the atomic structure into a coarse-grained structure of the molecule; training a denoised diffusion model using the coarse-grained molecular dynamics simulation data; generating, at the denoising diffusion model, a plurality of independent and identically distributed (iid) samples from an equilibrium distribution of the coarse-grained structure; and Output the multiple iid samples.

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