Abstract: A method for obtaining a refined model given a mis-specified symbolic model. The method includes receiving a mis-specified symbolic model and data pertaining to a process or phenomenon corresponding to the mis-specified symbolic model; receiving one or more constraints; generating a plurality of partial expression trees based on the mis-specified symbolic model; solving an optimization problem for each of the partial expression trees; and determining a refined symbolic model of the mis-specified symbolic model based on results of the optimization problem for each partial expression tree.

Abstract: Embodiments of the invention are directed to a programmable computer system having a processor system operable to perform processor system operations that include representing a set of candidate functions in a mathematical expression domain. The set of candidate functions defines relationships between data of an existing system. A set of known background theory is represented in the mathematical expression domain. The set of known background theory defines known relationships associated with the existing system. A model composition operation is performed that includes analyzing, in the mathematical expression domain, the set of candidate functions and the set of known background theory to generate a composed model that satisfies a target data fidelity in a manner that also satisfies a predetermined level of compatibility between the composed model and the set of known background theory.

Abstract: A method generates automated discovery of new scientific formulas. The method includes receiving a background theory associated with a phenomenon being studied. The processor receives a set of training data associated with the phenomenon being studied. The set of training data is processed in a machine learning model that generates candidate formulas from data points in the set of training data. Values of a numerical error-vector are generated for the candidate formulas. The candidate formulas are processed in a reasoning model. The operation of the reasoning model includes generating values of a theoretical error-vector based on the background theory. An output of a performance metric is generated based on a generalization of the theoretical error-vector and a reasoning error. The processor determines whether one of the candidate formulas is a meaningful and valid new scientific formula, based on a behavior of the reasoning error and the reasoning performance metric.

Abstract: Mechanisms are provided for automated rule set generation for identifying relations in knowledge graph data structures. An input knowledge graph is processed to extract tuples representing relations between entities present in the input knowledge graph. A set of rules is generated based on one or more heuristics applied to tuples, and candidate rule(s) are identified that are candidates for adding to the set of rules. A linear programming computer model is evaluated for a modified set of rules comprising the set of rules and the candidate rule(s) to determine whether or not adding the candidate rule(s) improves an objective function of the linear programming model. The set of rules is expanded to include the candidate rule(s) in response to the evaluation of the linear programming computer model indicating that the addition of the candidate rule(s) improves the objective function of the linear programming computer model.

Abstract: A processor may include a set of primitive operators, receive a set of data-driven operators, at least one of the set of data-driven operators including a machine learning model, and receive an input-output data pair set. Based on a grammar specifying rules for linking the set of primitive operators and the set of data-driven operators, the processor may search among the set of primitive operators and the set of data-driven operators to find a symbolic model that fits the input-output data set.

Abstract: A computer-implemented method for automatic multilabel classification includes receiving a label matrix Y for multiple training instances. The label matrix Y includes multiple labels, each label representing a respective category. The method further includes computing an intermediate matrix YYT, where YT is a transpose of the label matrix Y. The method further includes computing a basis matrix H by a non-negative matrix factorization of the intermediate matrix YYT. The method further includes generating a group testing matrix A by sampling the basis matrix H. The method further includes generating, for each training instance from the training instances, a reduced label vector z by computing a product of the group testing matrix A and a label vector y for respective training instance from the label matrix Y. The method further includes predicting multiple labels associated with an input based on the reduced label vector z.

Abstract: Aspects of the invention include obtaining a set of data that includes inputs and outputs to be modelled and performing a symbolic regression to find a symbolic model that fits the inputs and the outputs of the set of data. The symbolic model is a symbolic expression discovered by the symbolic regression in a search space. Automated reasoning is performed to affect a final symbolic model that is used to obtain new outputs from new inputs based on the final symbolic model.

Abstract: A processor may include a set of primitive operators, receive a set of data-driven operators, at least one of the set of data-driven operators including a machine learning model, and receive an input-output data pair set. Based on a grammar specifying rules for linking the set of primitive operators and the set of data-driven operators, the processor may search among the set of primitive operators and the set of data-driven operators to find a symbolic model that fits the input-output data set.

Abstract: A computer-implemented method for automatic multilabel classification includes receiving a label matrix Y for multiple training instances. The label matrix Y includes multiple labels, each label representing a respective category. The method further includes computing an intermediate matrix YYT, where YT is a transpose of the label matrix Y. The method further includes computing a basis matrix H by a non-negative matrix factorization of the intermediate matrix YYT. The method further includes generating a group testing matrix A by sampling the basis matrix H. The method further includes generating, for each training instance from the training instances, a reduced label vector z by computing a product of the group testing matrix A and a label vector y for respective training instance from the label matrix Y. The method further includes predicting multiple labels associated with an input based on the reduced label vector z.

Abstract: An automated method optimally designs plates to satisfy an order book at a steel plant so as to maximize the yield of the plates designed while using capacity fully to reduce the production of surplus slabs or plates, and satisfy order deadlines. Our method consists of four main components: (1) mother plate design, (2) slab design, (3) cast design, and (4) material allocation. A column generation framework for mother plate design is used where the problem is decomposed into a master problem and a subproblem. The master problem is used to evaluate packing patterns that should be used to fulfill the order book and the subproblem generates potential one-dimensional and two-dimensional feasible packing patterns as candidates to be evaluated by the master problem. The solution to the master problem produces a list of mother plates that need to be produced. These mother plates are transformed into candidate slabs, which are represented via an interval graph.

Abstract: An automated method optimally designs plates to satisfy an order book at a steel plant so as to maximize the yield of the plates designed while using capacity fully to reduce the production of surplus slabs or plates, and satisfy order deadlines. Our method consists of four main components: (1) mother plate design, (2) slab design, (3) cast design, and (4) material allocation. A column generation framework for mother plate design is used where the problem is decomposed into a master problem and a subproblem. The master problem is used to evaluate packing patterns that should be used to fulfill the order book and the subproblem generates potential one-dimensional and two-dimensional feasible packing patterns as candidates to be evaluated by the master problem. The solution to the master problem produces a list of mother plates that need to be produced. These mother plates are transformed into candidate slabs, which are represented via an interval graph.