Developing Density Functional Theory with Physical Prior Knowledge
Bibliographic record
Abstract
Density functional theory (DFT) has been used extensively over the past several decades and across many branches of science. The success of DFT lies in its relatively low-cost and usefully high accuracy in many practical systems of interest. However, there are still many instances, such as strongly correlated systems or systems at high temperatures, where conventional DFT approaches are no longer reliable. In addition, reliable DFT approaches are often computationally intractable for large system sizes, limiting their scope of application in realistic system settings. This dissertation is a collection of my contributions to address these fundamental challenges in the field. A common theme across all projects is the use of physical prior knowledge to motivate or (in)directly constrain the methods and techniques developed. In Chapter 1, I provide context for the research presented in the following self-contained chapters. Chapter 2 introduces condition probability DFT (CP-DFT) as a new and alternative density functional approach to obtain conditional probability densities and ground-state energies. Chapter 3 expands upon the previous chapter by establishing CP-DFT as a formally exact theory and derives several key physical properties of CP densities and corresponding potentials used in the theory. Chapter 4 analyzes and discusses the role of exact physical conditions (constraints) in developing conventional Kohn-Sham DFT exchange-correlation (XC) approximations. Chapter 5 introduces the Kohn-Sham regularizer method for training neural network-based XC models for strongly correlated systems. Chapter 6 expands on the previous chapter by developing a spin-adapted Kohn-Sham regularizer and demonstrating impressive generalizability on weakly correlated systems. Finally, Chapter 7 explores the repurposing of Tensor Processing Units – hardware designed for machine-learning tasks – for large-scale DFT calculations by utilizing algorithms that exploit physical properties of the density matrix.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.050 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".