Abstract: Example embodiments relate to machine-learned approximation techniques for numerical simulations. An example computer-implemented method for performing enhanced numerical simulations includes receiving a first vector field corresponding to a first solution of one or more differential equations at a first time step. The first vector field includes first values at each of a plurality of points along a mesh. The method also includes determining, using a machine-learned model, one or more refinement terms based on the first vector field, wherein the refinement terms represent effects of areas between points on the mesh. In addition, the method includes modifying one or more of the first values at one or more of the plurality of points along the mesh based on the one or more refinement terms. Further, the method includes generating a second vector field that includes second values at each of the plurality of points.

Abstract: The present disclosure is directed to a system for reparameterizing of a neural network to optimize structural designs. The system can obtain data descriptive of a design space for a physical design problem. The design space is parameterized by a first set of parameters. The system can reparameterize the design space with a machine-learned model that comprises a second set of parameters. For a plurality of iterations, the system can provide an input to the machine-learned model to produce a proposed solution. The system can apply one or more design constraints to the solution to create a constrained solution. The system can generate a physical outcome associated with the constrained solution using a physical model. The system can evaluate the physical outcome using an objective function and update at least one of the second set of parameters. After the plurality of iterations, the system can output a solution.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: A method for calibrating forecasts involving temperature, precipitation, and other weather related variables is provided. In an embodiment historical ensemble-based forecasts and historical observations are received by an agricultural intelligence computing system. Historical differences are determined between the forecasts and the observations corresponding to the forecasts and stored in the volatile memory of the agricultural intelligence computing system. The agricultural intelligence computing system receives current ensemble-based forecasts and a request for improved forecasts. The agricultural intelligence computing system retrieves the historical differences and uses a combination of the historical differences and the current ensemble-based forecasts to create probability distributions for the weather for each lead day. The agricultural intelligence computing system then samples from the probability distributions to create improved ensemble-based forecasts at the requested location.

Abstract: A method for temperature interpolation is provided. In an embodiment climatology records and temperature observations are received by a weather computing system over a network from an outside source. The temperature observations are subtracted from the climatology records to create anomalies. The anomalies are extrapolated across a map using various modeling methods and stored in the volatile memory of weather computing system. When the weather computing system receives a request for a temperature at a specific location, the weather computing system retrieves the anomaly field from the volatile memory and applies it to the climatology records at the requested location to determine the temperature for that location.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: In an approach, a method for fusing point data with areal averages is performed by a computing system. The fusion procedure is coherent, in the sense that the computing system takes into account what the areal averages represent with respect to the point data. The overarching goal is to fit a model that takes into account the information derived from both data sets. The areal averages provide an estimate for what the integral of a model representing the behavior of the environmental variable should be over a particular district and the point values indicate the estimated value at particular locations. Thus, the integral of the fitted model over a district of the grid should approximate the value provided by the areal averages while also approximating the value provided by the point data for locations which are provided by the point data.

Abstract: A method for calibrating forecasts involving temperature, precipitation, and other weather related variables is provided. In an embodiment historical ensemble-based forecasts and historical observations are received by an agricultural intelligence computing system. Historical differences are determined between the forecasts and the observations corresponding to the forecasts and stored in the volatile memory of the agricultural intelligence computing system. The agricultural intelligence computing system receives current ensemble-based forecasts and a request for improved forecasts. The agricultural intelligence computing system retrieves the historical differences and uses a combination of the historical differences and the current ensemble-based forecasts to create probability distributions for the weather for each lead day. The agricultural intelligence computing system then samples from the probability distributions to create improved ensemble-based forecasts at the requested location.

Abstract: A method for temperature interpolation is provided. In an embodiment climatology records and temperature observations are received by a weather computing system over a network from an outside source. The temperature observations are subtracted from the climatology records to create anomalies. The anomalies are extrapolated across a map using various modeling methods and stored in the volatile memory of weather computing system. When the weather computing system receives a request for a temperature at a specific location, the weather computing system retrieves the anomaly field from the volatile memory and applies it to the climatology records at the requested location to determine the temperature for that location.