## A Problem of Probability Density Function Estimation for Large Dimensional Spaces With Many Low-Influential Dimensions
*Jergus Suja, Martin Kubicek and Tomas Koutnik*

### Abstract
All engineering problems consider uncertainties. These range from small production uncertainties to large-scale uncertainties coming from outside, such as variable wind speed or sunlight. Currently, modern methods for uncertainty propagation have large difficulties with estimation of statistics for large-scale problems which considers hundreds of these uncertain parameters. Due to the complexity of the problem and limitations of the modern methods, a common approach for modelling large scale problems is to select a few important parameters and model statistics for these parameters. However, this can lead to an important problem. In this paper, an application of the UptimAI’s UQ propagation algorithm is used to discuss a new problem arising from very high dimensional spaces where a large number of parameters have negligible impact on the final solution. In other words, when a problem consists of a great number of uncertain design parameters, common practice is to focus on the most important ones and neglect the non-influential ones. However, a combination of a great number of noninfluential parameters can lead to completely different results. This is especially a problem for modelling large dimensional statistical models where a common approach is to perform sensitivity analysis and neglect the non-influential variables, i.e. set the non-influential variables to nominal value. Therefore, using a common approach of neglecting the non-influential variables could lead to a dramatic error and hence, we call this problem ”many times nothing killed a horse”. This problem cannot be observed for cases with a small number of design parameters, which are commonly solved in statistical modelling. The reason for this issue is that the combined influence of neglected variables is extremely small and such that has no influence on the final output. Application of the UptimAl’s UQ propagation algorithm to modern engineering problems and the possibilities of mitigation of the cumulative influence of non-influential parameters is discussed in detail. The problem is shown on a case of economic load dispatch (ELD) problem which consist of 140 dimensions [1]. To this problem was applied UptimAI’s UQ propagation algorithm to obtain accurate statistics for the problem and to get deeper insight into the statistics. Using the accurate model obtained by UptimAI’s algorithm, we compare statistics of using only important variables and using all variables. This lead to a significant difference between results and such that put a large question mark on standard approach. The obtained results are validated with the Monte Carlo simulation applied directly to ELD problem. Application of UptimAl’s UQ propagation algorithm to modern engineering problems and the possibilities of mitigation of the cumulative influence of non-influential parameters is discussed in detail.

Link to a full article [here](https://www.scipedia.com/public/Suja_et_al_2021a).

small_news13_image1.png

thumbnail_news13_image1.png

news13_image1.png

Problem of Large Dimensional Spaces

Take advantage of the current situation, invest in internal process improvement and be ready for upcoming market changes. **Market leaders see this rather difficult time as an opportunity to develop and become stronger.** Once the challenges are settled down, those who already implemented advanced technological and automated solutions will be the ones with a competitive advantage.

When almost the entire world is working from home and business may seem to slow down, making everything as effective as possible is crucial. From everyday tasks to top-level decisions, each activity is being re-evaluated for its actual value to the whole company and future steps. **Wrong decisions and double work are now more costly than ever. **The design process in manufacturing needs to be optimized to prevent failures that eventually lead to wasted resources.

**Our one-of-a-kind solution has proven to reduce design costs, scrap rates and to save many hours of work.** Being able to redistribute these resources smartly elsewhere is vital, especially in the present circumstances.

**We have shifted to fully remote mode and we are able to implement UptimAI virtually everywhere.** We are ready to help you fasten and optimize the design process. Take the first step today for an efficient process tomorrow.

[Get in touch with us and learn more](https://uptim.ai/). 

![news11_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news11_image2_74e6467f5e.png)


medium_news11_image1.jpg

small_news11_image1.jpg

thumbnail_news11_image1.jpg

news11_image1.jpg

Why invest in AI technology now?

The evolution of the UptimAI software has begun at the University of Strathclyde in Glasgow, where its prototype was used by researchers to identify impact trajectories of the space debris. **For the first time, it became possible to create complex mathematical models with an even lower amount of simulations than is the number of problem parameters.** To prove technology’s abilities on practical engineering problems, it was used for the analysis of the novel design of the flapped airfoil for commuter aircraft. The model of the problem created by UptimAI confirmed that the proposed flap concept has large potential to **improve** the airplane’s flight performance and shorten the landing distance. Compared to commonly used Design of Experiments methods, the UptimAI approach **saved more than 450 hours of computational time.** Moreover, it allows designers to easily find the direct way to stable aerodynamic characteristics which can be relied upon even if the flap is being deformed under loading. The article was written by CzechInvest with the help of our Head of Application, Tomáš Koutník.

Read the full article [here](https://www.czechinvest.org/en/Homepage/News/September-2020/What-does-space-do-for-the-aero?fbclid=IwAR2l9jMvcs-aW81prkCUC6tLFfqYZHgJWSrHOOMIUK1AETcaFF3uHawAIA4).

*Source: European Space Agency*

![news10_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news10_image2_abc53e66c3.png)



medium_news10_image1.jpg

small_news10_image1.jpg

thumbnail_news10_image1.jpg

news10_image1.jpg

What does space do for the aero?

The whole project started as an off-spin of Martin’s projects during his PhD studies at Starthclyde University. This new algorithm for the propagation of uncertainties was based on a fundamentally new approach to meta-modeling (https://en.wikipedia.org/wiki/Metamodeling), which was later targeted to engineering problems. It turned out that the developed code was very efficient and very robust. Moreover, the technique provided some new insight into the problem and helped to inform a deeper understanding of the problem. It’s first application was the uncertainty propagation for re-entry of orbital debris, where it has shown the importance of statistical propagation. Results clearly showed that a common assumption of ‘Plus-minus’ around the result is completely wrong as you can see in the picture below.

![news01_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news01_image1_d85650400c.png)

The statistics have a profound influence on the expected result and sometimes it can create some famous quotes such as ‘Houston, we have a problem’. Well, engineers were probably not very happy about this infamous space catastrophe.Moreover, the result was something unexpected even for the team who was working on the re-entry case. We tested the result with an experiment by throwing small balls into the air and observing their impact locations. It turns out that the results of the experiment were very similar to our algorithm, which proved that our algorithm worked very well.

The second case was the re-entry of GOCE and its flight parameters . Here again the algorithm showed its strengths and some interesting ‘wow’ moments about the re-entry. However, it showed a very important aspect of the algorithm, that it can work very efficiently for virtually any problem. Hence, it was decided to transform the algorithm into something industry can use to improve their products.

In the first year, the algorithm started to change to suit industrial needs. It was a very turbulent time, but after many hours of programming, testing and developing, an improved version of the algorithm was created. This new algorithm was used for the collapse of the car box-beam, which was done in cooperation with MECAS ESI in Pilsen. Again, the algorithm proved its robustness and showed that it is working very well even for such complex cases. More importantly, we came up with some interesting ideas on how to provide engineers with even deeper insight. This case impressed Skoda Auto and we started to cooperate on passive safety of cars.

After the first year and with a successful application of our code in industry, we were accepted into ESA Incubator in Prague (http://www.esa-bic.cz). Empowered with new ideas, experienced with industrial problems and full of enthusiasm, we started to develop a new industry target platform. After two years of successful incubation, we can proudly say that we developed a tool, which can tackle even the most difficult cases with an efficiency never seen before. Moreover, apart from standard analysis, our tool provides unique insight, which is only available due to our unique approach. Our tool already helps engineers to develop a product, which is more reliable, efficient and ahead of it’s competition.

Today, industry and academia are using our tool, but we will not stop there. We have plenty of new ideas on how to improve our code in its efficiency and even more ideas on how to provide engineers additional insight to produce a better product – so stay tuned.


thumbnail_news01_image2.png

news01_image2.png

The story behind Uptimai

Blog

We are happy to share that we have been nominated as one of the top Machine Learning companies in the Czech Republic by Best Startup EU!

In the published article, Best Startup EU picks the companies that are taking approaches to innovate the Machine Learning industry in all kinds of industries, and selects the companies that excel in one of these categories:
- Innovation
- Growth
- Management
- Societal impact

You can read the full article [here](https://beststartup.eu/41-top-machine-learning-startups-and-companies-in-czech-republic/).

medium_news16_image1.jpg

small_news16_image1.jpg

thumbnail_news16_image1.jpg

news16_image1.jpg

Top ML company in Czech Republic

Uptimai has been selected as one of the 28 most innovative Czech Republic companies that use Machine Learning Technology by Futurology Life.

Futurology Life is a media company based in London that aims to boost inbound investment into innovative companies and startups by addressing the information asymmetry between small innovative startups and institutional investors.

The companies were selected by their performance in the following categories: Innovation, Growth, Management and Social Impact.

You can check the complete article for more information [here](https://futurology.life/28-most-innovative-czech-republic-based-machine-learning-companies/).

![news15_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news15_image2_6966c9ce19.png)



small_news15_image1.png

thumbnail_news15_image1.png

news15_image1.png

Innovative Machine Learning Company

Our CEO Martin Kubicek and Head Developer Jiri Otoupal visited the University of Defense in Brno. During the visit our team made a presentation to show the capabilities of our software and engineering team. Our cutting-edge Uncertainty Quantification approach leads to deeper insights and better designs for all the different performance conditions for both civil and military purposes.

Events like this one allows to create links between the civilian and the military industry, and to reinforce our commitment with the academia.

![news14_image2.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/news14_image2_7435b1c7b4.jpg)



small_news14_image1.png

thumbnail_news14_image1.png

news14_image1.png

Visit to the University of Defense

Our CEO Martin Kubicek and Head Developer Jiří Otoupal attended the third **Czech-American Defense and Cybersecurity Forum in Prague.**

In the beginning, Deputy Minister Kopečný and many other government & security officials emphasized how useful and important these regular meetings are. **If companies want to keep pace in technological progress they have to find a way to collaborate with a variety of organizations** and such events are a great way to do so.

The event was designed to strengthen bilateral cooperation between the US and the Czech Republic. It brought together the U.S and Czech defense suppliers with senior defense and industry leaders **to share important information, and to forge and develop new connections.** The collaboration between the two countries is obviously paying off because the export of military materials is **increasing in the last decade.**

It was a high-profile opportunity for us so we are glad that we were given the opportunity to take part.

![news12_image1.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/news12_image1_57b3f2ae7c.jpg)
*Our staff and ambassador Stephen B. King*

large_news12_image2.png

medium_news12_image2.png

small_news12_image2.png

thumbnail_news12_image2.png

news12_image2.png

Czech-American Defense and Cybersecurity Forum

The world is dealing with the global pandemic longer than we expected and the impact of COVID-19 is inevitable. Although the times are unpleasant and connected to a lot of potential obstacles **it is necessary to be even more creative and effective.** We are at that point, where the production is in a state of stagnation but the new products need to be in the continual process of development. **Constant innovation is crucial when it comes to the long-term survival of a business.**

All of us have to be in some way prepared for future events and think further when the situation will get better. That’s the reason why we decided to step up to help in these difficult times by **making our product more affordable, and accessible to support your development and be part of your success.**

Today´s post is dedicated to an **exclusive discount**. How does it work? **We offer a 60 % off subscription fee for all new SME clients (up to 500 employees)** for the first year without any commitments. [Request a demo](https://uptim.ai/) and we will be happy to provide you more information.


small_news09_image1.png

thumbnail_news09_image1.png

news09_image1.png

COVID-19 SMB Discount

We are happy to announce that UptimAI has become a part of **Composites United cluster!**

Composites United is a Berlin-based association for **sustainable fiber-based multi-material lightweight construction** with a farseeing vision and a progressive mission. The cluster brings together about 400 members from various industries, regions and countries, united by the same goal of developing new approaches and solutions for fiber-based constructions. A membership in the Composites United clusters gives members the opportunity of participation in research and development projects, access to new international markets, help with funding and promotion and many more.

The main goals of UptimAI as fresh members are cooperating with the wide network of Composites United, meeting **new potential partners and clients**, and presenting to them our **cutting-edge solution**.

Check the [Composites-United website](https://composites-united.com/).

Learn more about [how our solution works](https://uptim.ai/) and request a demo to give it a try!

![news08_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news08_image1_cbee1d6a25.png)


small_news08_image2.png

thumbnail_news08_image2.png

news08_image2.png

We are a member of Composites United!

UptimAI company was incubated in the **European Space Agency Business Incubator** in Prague to enable the use of our cutting-edge algorithm for a wide range of industrial applications. **At the moment, we are able to connect UptimAI with any CAE simulation platform without any limitations.** In cooperation with ESA BIC Prague, we created a video to show you our Uncertainty Quantification solution in more detail.

[Get in touch](https://uptim.ai/) with us to discuss possible use-cases for your CAE challenges. **You will be amazed by the efficiency of our product!**

![esa-bic-video](https://uptimai-website.s3.eu-central-1.amazonaws.com/ESA_UPtimAI.mp4)
Video: [https://www.youtube.com/watch?v=dEKTxXobQDg](https://www.youtube.com/watch?v=dEKTxXobQDg)






small_news07_image1.png

thumbnail_news07_image1.png

news07_image1.png

ESA BIC Prague introduces UptimAI

UptimAI was shortlisted for the TOP30 in a startup competition organized by Vodafone. It is a really great opportunity for us to show our solution to the jury and get feedback from experienced entrepreneurs. **Additionally, there is a chance to win valuable prizes or up to €3.75M investment!**

More information about the competition can be found [here](https://napadroku.cz/en/). **Wish us luck! **

![news06_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news06_image1_74d27fec98.png)


thumbnail_news06_image2.png

news06_image2.png

Vodafone Idea of the Year TOP30

We got into PowerUp! Country Final Czechia, where 8 startups are going to pitch and compete to advance to Grand Final, multi-million Euro investments, and wide support from InnoEnergy.

PowerUp! is the challenge for start-ups, scale-ups, and SMEs from Central and Eastern Europe whose products in the fields of energy, smart technologies, mobility are solving today’s problems with tomorrow’s technology.

Who to expect? Ibatt.energy, BatteryCheck, ENMON Technologies, Pocket Virtuality, UptimAI, Topíte, Skymaps, and Mileus.

**[REGISTER for the event](https://www.eventbrite.com/e/virtual-powerup-country-final-czechia-tickets-102906020678) to save your spot.** Even the online seats are limited!

![news05_image2.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/news05_image2_9d680a3469.jpg)


thumbnail_news05_image1.png

news05_image1.png

PowerUp! Country Final

We are honored to announce that we will take part in **Industry Space Days 2020 (ISD).** This virtual event will take place on 16-17th September 2020.

The ISD is an event organized by ESA which brings together **important European players in the space sector through B2B meetings and conferences.**

The main purpose is to connect and increase involvement in space activities. Companies are encouraged to share their visions and ideas to produce better results. So it provides us a **great chance** to introduce our product, meet potential clients, or create new business collaboration.

Stay tuned and catch us there!

Check the official websites [https://isd.esa.int/](https://isd.esa.int/)

![news04_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news04_image2_b1eb36114d.png)


small_news04_image1.jpg

thumbnail_news04_image1.jpg

news04_image1.jpg

ISD SPACE DAYS 2020

We’ve been named one of **@hellotmrc**’s Deep Tech Pioneers, from over 5,000 applications from 128 countries!

HELLO TOMORROW is an organization that identifies, and analyses innovation trends & dynamics leveraging experts. It connects the best minds and builds a worldwide community of science entrepreneurs, investors, corporates and academics to work together to untap the enormous potential of deep technologies. The most anticipated technology event in the world will happen this fall and we will be a part of the Deep Tech week.

Upcoming Summit will cover four major topics: Space, Planet, Human and Machine.

**Come and meet us at the Hello Tomorrow Global Summit in Paris on the 12th – 13th of March 2020!**

**EDIT: POSTPONED TO 22nd – 23rd of October 2020.** We will keep you posted. **<u>[Find more information here](link)</u>**

![news03_image2.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/news03_image2_8110be2b08.jpg)


small_news03_image1.png

thumbnail_news03_image1.png

news03_image1.png

We are Deep Tech Pioneers!

At the end of 2019, we participated in an acceleration program that supported our company’s growth significantly. With the investment from Lighthouse Ventures, we have been able to advance the tool development, rebrand and expand the business.

“**Martin Kubíček has developed a unique product that is ten times faster and significantly more accurate than similar solutions on the market.** Thanks to our acceleration the program, we want to help him turn technology into business success on the international market,” explained Michal Zálešák, the Managing Partner at Lighthouse Ventures.

UptimAI offers full automation and simple connection to standard simulation tools. This leads to high efficiency while offering deeper insights and a different perspective on product optimization. **This is a revolution for the simulation area.** One tool that combines an otherwise lengthy process of simulation set-up, code synchronization, and the creation of a simplified model. Thanks to the unique algorithm, for example, engines are more efficient, cars safer or bridge structures more stable. The solution can be applied in a wide range of industries. Use for the solution can be limitless, for instance, aircraft and spaceships manufacturing, engineering and medicine.

“Since we are engineers by profession, **we understand that existing optimization methods are not applicable to conventional engineering designs.** Instead of a clear optimum, our algorithm will offer the engineer a wider field of choice, which is much more practical than the standard approach,” says Martin.

One of the successful pilot projects that was our jump start for the investment was executed for Škoda Auto in Mladá Boleslav, where our startup worked on the so-called box beam. This is the part of the car that absorbs impact energy and significantly increases the chances of survival in an accident.

“We helped to improve the element to be resistant to many directions of impact and not just to the front impact. We also helped set the element so that its absorbed energy is not affected by external circumstances,” says Martin. Since the pilot, we have continued our cooperation with Škoda.

The article was written by Czech Crunch, which interviewed Martin Kubíček, the founder of UptimAI.

**Read the full article [here](https://cc.cz/vyvinul-algoritmus-ktery-pomaha-skodovce-a-zachranuje-zivoty-ted-na-nej-martin-kubicek-ziskava-miliony-korun/)** (Czech version only).

![news02_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news02_image2_c1147d211c.png)


News & Blog

News