Recently, I had a chance to be in a room with a bunch of Ph.D. students and faculty members from the mechanical engineering department. Faculty members were presenting their research to other faculty members and Ph.D. students.

I quickly noticed that regardless of whether someone was an experimentalist, a theorist, or a numerical person like me, there were always slides showing results from numerical simulations. Some people prefer to call them computer simulations.

At the end of the event, there was a 30-minute slot for all scholars to discuss anything they liked. No one raised any questions. It was quiet. So I decided to throw out a question to start some discussion: how confident are you in your computer simulations?

I raised this question because I am not fully confident in any numerical simulation result I produce. Don’t get me wrong. I’m not attacking computer simulations, and I am a pure numerical guy. I was a simulation engineer in industry in the past, and now I am a Ph.D. student in numerical methods in academia.

But I have always had this question in my mind because of a past experience. A long time ago, before I returned to academia, I was a simulation engineer in the manufacturing industry. I used my skills to provide suggestions to customers regarding various problems during manufacturing processes.

Once, a customer came to me and wanted me to run simulations for a problematic mold they had. Usually, in a case like this, computer simulation is just a tool to help us design solutions, and we still need experiment-based tests to confirm them.

But this case was urgent. The customer had no time to do careful examinations or tests. So they were going to modify their mold based only on my simulations. They told me the modification would cost one million dollars, and they had only one shot. So they wanted me to make sure the simulation results were correct.

When I heard that the modification would cost one million dollars, I freaked out. I simply could not guarantee that the simulations were accurate enough. I was not confident enough because, as someone trained in numerical simulation, I know how many uncertainties and errors are involved.

So I just could not tell them, “Yes, just trust the simulations and go ahead with the modification.”

Ever since then, whenever I see someone showing results from computer simulations, I always want to ask whether they are confident enough in those simulations if one million dollars were to be spent based solely on those results, without any further experiment-based tests.