Understanding AI's Capabilities

The realm of artificial intelligence, particularly ChatGPT, piques my interest immensely. What functionalities does it possess? What are its shortcomings? How practical is it for daily tasks?

We’ve explored some of these aspects in a prior article. However, my quest for deeper insights revealed something quite shocking. The gravity of a specific flaw necessitates our attention today.

Image by Clker-Free-Vector-Images on pixabay. ChatGPT logo by OpenAI. Edited by an uncreative author.

To provide context for my inquiry, I had a conversation with ChatGPT about a technical subject. I explained my use of the discontinuous Galerkin (DG) method for simulating a resonant tunneling diode (RTD). The RTD is modeled by the Liouville-von Neumann equation, which predicts electron transport within an electrical nano-structure. In essence, I utilize the DG method to tackle this equation.

The DG approach, derived from the Finite Element Method (FEM), operates within computational domains. Consequently, our RTD becomes a one-dimensional issue with two computational coordinates. One of these domains extends infinitely due to the one-dimensional discretization, resulting in open boundaries at its edges. As a result, reflections of electrons would appear in our final solution, an impossibility since the device extends infinitely in that direction. To address this, we introduce a complex absorbing potential (CAP) that effectively absorbs the electrons at the boundaries, correcting their behavior.

Next, I wanted to see how ChatGPT would respond to my question about complex absorbing potentials.

“Are you familiar with complex absorbing potentials?” I asked.

“Yes, I am! They are utilized in computational physics and chemistry to model particles or waves nearing an absorbing boundary, especially in scattering scenarios. The concept involves integrating an imaginary potential that diminishes exponentially as the particles approach the boundary. This imaginary aspect is superimposed on the original potential, forming a region where the wave function or particle density is suppressed, thereby minimizing any reflection or interference at the boundary.”

This explanation provided a deeper understanding of CAPs, but I was curious about their origins. I proceeded to ask ChatGPT who conceptualized them.

“The notion of complex absorbing potentials was first put forward by E.B. Norman and R.W. Joynt in their 1979 paper titled ‘Complex Potential Approach to Scattering in Three Dimensions.’ This work outlines a method for simulating particle behavior near an absorbing boundary via an imaginary potential that dampens the wave function,” it claimed.

At first glance, this answer seemed plausible. However, upon searching for the cited paper, I found… nothing.

In an ideal scenario, one would recognize the absence of this citation when attempting to reference it in their own work. Yet, fabricating a nonexistent paper in a serious tone is deeply unethical. While seasoned researchers tend to fact-check statements, consider a younger student diligently compiling their thesis. When reviewed by a professor with decades of experience, the sight of a “new” paper from 1979 would understandably raise eyebrows, jeopardizing the entire thesis.

This should not be the norm. Regardless of age, students must adhere to best research practices, yet many prioritize obtaining their degree over engaging in genuine research.

I confronted ChatGPT regarding the misinformation, and it replied:

“I apologize for the mistake in my earlier response. My intention was not to mislead. Upon further examination, I discovered that the concept of complex absorbing potentials was actually introduced by M.V. Berry and K.E. Pringle in their 1972 paper titled ‘Asymptotic theory of internal modes in inhomogeneous media.’ This work discusses a method for integrating an absorbing boundary condition into the wave equation using an imaginary potential that diminishes as the wave function nears the boundary.”

Once again, I conducted a search and… drumroll… the paper did not exist either. Upon questioning ChatGPT about this second error, its response was:

“I sincerely apologize for the incorrect information once more. After further investigation, I found that the concept of complex absorbing potentials was first proposed by C. Zener in his 1932 paper ‘Non-adiabatic crossing of energy levels.’ Zener introduced a method to incorporate an imaginary component into the potential energy to model non-adiabatic transitions.”

Though this paper is indeed real, it has no connection to complex absorbing potentials. Frustrated, I abandoned my search for the correct origin of the term. The earliest credible reference I could find regarding complex absorbing potentials was a 1986 paper by R. Kosloff and D. Kosloff, titled “Absorbing Boundaries for Wave Propagation Problems,” which thoroughly explains the purpose and mechanics of CAPs.

The ability to fabricate papers or information to address inquiries, regardless of the context, is a concerning characteristic for an AI that aspires to achieve general intelligence. It would be prudent for OpenAI to implement mechanisms allowing the model to acknowledge its limitations instead of misleading users.

For these reasons, I strongly advise against relying on ChatGPT for serious academic work. Moving forward, I will also avoid using it as a starting point for my blog posts.

I hope this insight helps others maintain their credibility within the academic community.

Exploring My Journey

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Chapter 2: Video Insights on ChatGPT's Impact

In the first video, titled "ChatGPT: A Game Changer for Researchers?" the presenter explores how ChatGPT can assist in research, showcasing its capabilities and limitations.

The second video, "DON'T TRUST ChatGPT's CODE!" delves into the reliability of code generated by AI, emphasizing the need for careful scrutiny.