# US 12,217,152 B1 · Systems and methods for using deep machine learning for evolving boundary condition problems > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,217,152 B1 - Document ID: US12217152B1 - Status: Granted - Kind: B1 - Application number: 17/248,657 - Filed: 2021-02-02 - Granted: 2025-02-04 - Earliest claimed: 2021-02-02 - Assignees: Wells Fargo Bank, N.A. - Applicants: Wells Fargo Bank, N.A. - Inventors: Narayan Ganesan; Yajie Yu; Bernhard Hientzsch - Web page: https://patentgrep.com/patent/US12217152B1 ## CPC - G06N 3/047: Probabilistic or stochastic networks - G06F 16/9024: {Graphs; Linked lists (G06F16/9027 takes precedence)} - G06N 3/08: Learning methods - G06N 3/084: Backpropagation, e.g. using gradient descent - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract Systems, apparatuses, methods, and computer program products are disclosed for determining and providing value information and/or boundary activation information for a system defined in an at least partially bounded domain (i.e., the boundary of said domain consisting of at least one point) and having boundary conditions imposed at a boundary thereof. A deep BSDE solver is trained by, for each time step and for each path, determining, based on a set of underlying features for that path, whether a boundary condition has been activated for the path. When it is determined that a boundary condition has been activated for a first time for the path, an output value for the path is updated based on the boundary condition, an output time is updated based on the boundary activation time step, and not updated further. When the boundary condition was not activated for the path by the final time, the output value for the path is a final corresponding value. ## Claims ### Claim 1 A method for determining and providing value information and/or boundary activation information for a system defined in an at least partially bounded domain and having boundary conditions imposed at a boundary of the bounded domain, the method comprising: determining, by one or more processors, a plurality of paths for the system through at least a portion of the bounded domain based on an initial set of underlying features and a path evolution determined for each path, each path corresponding to a set of times comprising an initial time, a final time, and one or more intermediate times between the initial time and the final time, wherein the set of underlying features corresponds to respective financial values of a set of assets; causing, by the one or more processors, a deep backward stochastic differential equation (deep BSDE) solver to be trained until a convergence requirement is satisfied by: for each time step and for each path: determining the set of underlying features and a value corresponding to the set of underlying features, determining, based on the set of underlying features, whether a boundary condition has been activated for the path, and when it is determined that the boundary condition has been activated for a first time for the path, updating an output value for the path based on the boundary condition and an output time based on the time step at which the boundary condition was activated for the path, when the boundary condition was not activated for the path prior to the path reaching the final time, updating the output value for the path based on a final value corresponding to the set of underlying features at the final time, defining a set of output values comprising the output value for each path and determining one or more statistical measures of spread based on the set of output values, and modifying one or more parameters of a DNN of the deep BSDE solver based on the one or more statistical measures of spread; after the convergence requirement is satisfied, determining, by the one or more processors, at least one of (a) value information comprising a value corresponding to the system at the initial time and/or at one or more intermediate times based on the values and features for each path or (b) boundary activation information comprising a likelihood of boundary activation; causing, by the one or more processors, at least a portion of the at least one of (a) value information or (b) boundary activation information to be provided such that a user computing device receives the at least a portion of the at least one of (a) value information or (b) boundary activation information and provides a representation of the at least a portion of the at least one of (a) value information or (b) boundary activation information via an interactive user interface provided via a display of the user computing device; and causing, by the one or more processors, purchase of a portfolio comprising the set of assets based on the at least a portion of the at least one of (a) value information or (b) boundary activation information. ### Claim 2 (depends on 1) The method of claim 1, wherein the value corresponding to the system at the initial or one or more intermediate times is determined by the DNN and comprises at least one of (a) a numerical value or (b) an expression for the value corresponding to the system at the initial time as a function of the initial set of underlying features. ### Claim 3 (depends on 1) The method of claim 1, wherein the likelihood of boundary activation comprises at least one of (a) a numerical value, (b) an expression for the likelihood of boundary activation as a function of the initial set of underlying features, or (c) an expression for the likelihood of boundary activation as a function of time. ### Claim 4 (depends on 1) The method of claim 1, wherein the deep BSDE solver is a computational graph comprising nodes dedicated to evaluating the boundary condition at each time step based on the set of underlying features at the time step. ### Claim 5 (depends on 1) The method of claim 1, wherein once the output value for the path has been updated and the output time for the path has been updated based on a determination that the boundary condition has been activated for the first time for the path, preventing further updating of the output value and the output time for the path. ### Claim 6 (depends on 1) The method of claim 1, wherein the boundary condition comprises at least one of an upper boundary or a lower boundary for the set of underlying features or the value corresponding to the set of underlying features. ### Claim 7 (depends on 1) The method of claim 1, wherein the boundary condition evolves with time. ### Claim 8 (depends on 1) The method of claim 1, wherein the one or more parameters of the DNN are modified using a stochastic gradient descent training model. ### Claim 9 (depends on 1) The method of claim 1, wherein the DNN comprises a plurality of sub-networks, each sub-network corresponding to a date of a set of dates. ### Claim 10 (depends on 1) The method of claim 1, wherein the DNN is a feedforward DNN. ### Claim 11 An apparatus for determining and providing value information and/or boundary activation information for a system defined in an at least partially bounded domain and having boundary conditions imposed at a boundary of the bounded domain, the apparatus comprising: processor circuitry configured to: determine a plurality of paths for the system through at least a portion of the bounded domain based on an initial set of underlying features and a path evolution determined for each path, each path corresponding to a set of times comprising an initial time, a final time, and one or more intermediate times between the initial time and the final time, wherein the set of underlying features corresponds to respective financial values of a set of assets; cause a deep backward stochastic differential equation (deep BSDE) solver to be trained until a convergence requirement is satisfied by: for each time step and for each path: determine the set of underlying features and a value corresponding to the set of underlying features, determine, based on the set of underlying features for that path, whether a boundary condition has been activated for the path, and when it is determined that a boundary condition has been activated for a first time for the path, update an output value for the path based on the boundary condition and an output time based on the time step at which the boundary condition was activated for the path, when the boundary condition was not activated for the path prior to the path reaching the final time, update the output value for the path based on a final value corresponding to the set of underlying features at the final time, define a set of output values comprising the output value for each path and determining one or more statistical measures of spread based on the set of output values, and modify one or more parameters of a DNN of the deep BSDE solver based on the one or more statistical measures of spread; after the convergence requirement is satisfied, determine at least one of (a) value information comprising a value corresponding to the system at the initial time and/or at one or more intermediate times based on the values and features for each path or (b) boundary activation information comprising a likelihood of boundary activation; cause at least a portion of the at least one of (a) value information or (b) boundary activation information to be provided such that a user computing device receives the at least a portion of the at least one of (a) value information or (b) boundary activation information and provides a representation of the at least a portion of the at least one of (a) value information or (b) boundary activation information via an interactive user interface provided via a display of the user computing device; and cause purchase of a portfolio comprising the set of assets based on the at least a portion of the at least one of (a) value information or (b) boundary activation information. ### Claim 12 (depends on 11) The apparatus of claim 11, wherein the value corresponding to the system at the initial or one or more intermediate times is determined by the DNN and comprises at least one of (a) a numerical value or (b) an expression for the value corresponding to the system at the initial time as a function of the initial set of underlying features. ### Claim 13 (depends on 11) The apparatus of claim 11, wherein the likelihood of boundary activation comprises at least one of (a) a numerical value, (b) an expression for the likelihood of boundary activation as a function of the initial set of underlying features, or (c) an expression for the likelihood of boundary activation as a function of time. ### Claim 14 (depends on 11) The apparatus of claim 11, wherein the deep BSDE solver is a computational graph comprising nodes dedicated to evaluating the boundary condition at each time step based on the set of underlying features at the time step. ### Claim 15 (depends on 11) The apparatus of claim 11, wherein once the output value for the path has been updated and the output time for the path has been updated based on a determination that the boundary condition has been activated for the first time for the path, preventing further updating of the output value and the output time for the path. ### Claim 16 (depends on 11) The apparatus of claim 11, wherein the boundary condition comprises at least one of an upper boundary or a lower boundary for the set of underlying features or the value corresponding to the set of underlying features. ### Claim 17 (depends on 11) The apparatus of claim 11, wherein the boundary condition evolves with time. ### Claim 18 (depends on 11) The apparatus of claim 11, wherein the one or more parameters of the DNN are modified using a stochastic gradient descent training model. ### Claim 19 (depends on 11) The apparatus of claim 11, wherein the DNN comprises a plurality of sub-networks, each sub-network corresponding to a date of a set of dates. ### Claim 20 (depends on 11) The apparatus of claim 11, wherein the DNN is a feedforward DNN.