Uptimai software package
To provide complete services in the field of mathematical modelling, Uptimai develops its own state-of-the-art tool for Uncertainty Quantification (UQ), Data Analysis and Statistical Optimization (SO) which combines the results of our research with elements of machine learning. Originally used for orbital mechanics, now it is ready to be used in any type of R&D. It automates the whole process of mathematical modelling and provides the solved problems with deep insights that are easily readable. Thus, anyone can use the benefits of sophisticated mathematics without being an expert.
Preliminary analysis
Uptimai software allows to obtain very rapidly the sensitivity analysis, without the need for a large dataset. The sensitivity analysis shows the relevance of each parameter by themselves, but also which interactions between multiple parameters are significant. That allows identifying negligible variables before a complete study of the problem is done, reducing the cost of the model.
Uncertainty quantification
The most used methods of analysis, planning, or design are often based on a specific set of assumptions or considerations, which lead to the final result. However, in the real world the conditions are rarely constant, the environment is changing, products can have various shapes with tolerances, and also human work is prone to errors. Uncertainty quantification evaluates how all these changes (here called uncertainties) affect the observed result. It can identify important variables and how they interact with each other. Also, it clearly shows what are the current limits of the task and the way to improvements.
Surrogate modeling
For purposes of analyses and optimizations, we replace the observed data with its surrogate mathematical model. It describes dependencies between input variables and outputs. Unlike the others, our method includes the own-developed interpolation techniques to handle highly discontinuous problems. Results of a precise surrogate model are equivalent to the real-world data, allowing to observe trends and other phenomena with much lesser costs than in the case of full-scale measurements or time-consuming simulations, making parametric studies and other analyses feasible and more valuable.
Machine learning
Uptimai Algorithm incorporates advanced machine learning methods to adapt automatically to the task. Our approach ensures that each sample is used as efficiently as possible. The result is the most precise mathematical model built for the minimal cost, saving 30-90% of data required to create a comparable model using standard DOE methods and similar solutions.
Data analysis
Uptimai is capable of creating the mathematical model from existing data as well. This allows the processing of all the results obtained from either previously computed simulation runs or experimental data from various measurements. Then, the mathematical model can be analysed in detail and worked within the Uptimai tools, using all its features and benefits.
Multiobjective Optimization
After the model being build, Uptimai software has a multiobjective optimization tool, using state-of-the-art algorithms that allows visualizing where the absolute optimum inside the study range is. Thanks to our innovative technology we find the optimum with a fraction of the usually needed simulations.
Statistical optimization
The models and methods we use allow us to perform a new type of robust optimization based on the statistics. Instead of optimizing towards a single point, this method recommends ranges of input parameters always leading to an increase in the performance of the product under all operating conditions, respecting tolerances, etc. It is also well suited for multiobjective problems, where all the necessary trade-offs can be done just by a simple comparison of graphical outputs.
Benefits
New Insights
Allows to see roots of the solved problem to get the decision-making process knowledge-based.
Robust solutions
Suggests a clear path to statistically reliable improvements resistant to changes in conditions.
Lower costs
Saves up to 90% of the development time compared to standard approaches or DoE methods.
Custom features
Uptimai is not just the software, but also the team of skilled mathematicians, developers, and engineers. To satisfy specific needs of our clients, we are able to customize our methods to fit their projects.
