Thank the host. The invitation asked for three things: crucible, pounce and discopt, and my experience working with Claude. This talk is all three, organized around the differentiable optimization landscape we have been building this year. Caveat up front: I am a chemical engineer who learned optimization by building it. Many of you know these algorithms far better than I do; I am here to show what is now possible for someone like me, and to hear where I got it wrong.

~1 min. Each dot is a paper; size ~ citations. 2002-08 DFT surface science; 2009-15 CO2 capture, oxides; 2016- ML for simulation; 2021- optimization, automation, AI for science. The constant thread is software that makes the science faster. The new part this year: solvers.

people

scimax: interface

agent

knowhow: knowledge

crucible: memory

lab and compute

The picture: people stay in charge and talk to the agent through scimax, where we already write notes, code and papers. The agent gets our know-how from skills (knowhow), remembers across sessions through crucible, and acts on the lab and compute through tools like discopt-doe and the Opentrons skill. The next slides take each piece in turn.

Inspired by Karpathy's LLM knowledge-base pattern. The wiki is the agent's domain; I rarely edit it. Each conversation adds up instead of evaporating. Every project (including MFI) has its own crucible; a CLAUDE.md directive tells the agent to check it before answering domain questions. Useful for proposals, student meetings, lab notebooks.

knowhow is the tool and a collection. Any git repo with SKILL.md files works, so a group can publish its own lab's skills and students install them in one line. Compatible with npx skills. Safety: shows hook and MCP scripts before installing. Offer: happy to help anyone write skills for their own instruments or courses.

I never knew TypeScript or VS Code internals; Claude Code made it possible to port scimax in a few weeks, extended to Markdown and LaTeX. I use it nearly daily. The broader point: agents let domain experts build real software tools. Install from the VSIX on GitHub releases.

The landscape post (kitchingroup.cheme.cmu.edu/posts/differentiable-optimization-landscape) is the written version of this section.

Three columns. Programs: write ordinary Python + JAX (difflow), sequential modular. Equations: an algebraic modeling language (discopt) with modules and plugins, simultaneous. Solvers in the middle are shared: feral -> pounce -> discopt, plus jax-go which certifies global bounds directly on JAX programs. Surrogates with UQ along the bottom feed both sides: as JAX callables in programs, as embedded constraints in equation models. Hover to show the details live.

Started right after Opus 4.5 (Nov 2025); proof of concept in days. Learned about sequential modular vs simultaneous the practical way. The IDAES comparison is from the NNL rare-earth cascade work.

GRC Catalysis, Feb 2026: I said as a community we were not thinking big enough. I did not know Rust or interior point methods well. Many people did not think it would work. The first attempt (ripopt) had to be abandoned; the second is feral + pounce.

scimax-hidden ## Interior point methods in one slide (for me, not for you) Log barrier, $\mu \to 0$: $\displaystyle \min_x \; f(x) - \mu \sum_i \ln s_i \quad \text{s.t.} \quad c(x) = 0$ Each Newton step solves the KKT system $$ \begin{bmatrix} W + \Sigma + \delta_w I & J^\top \\ J & -\delta_c I \end{bmatrix} \begin{bmatrix} \Delta x \\ \Delta \lambda \end{bmatrix} = - \begin{bmatrix} \nabla_x \mathcal{L} \\ c(x) \end{bmatrix} $$ <div class="cols small"> <div> - Sparse, symmetric **indefinite**, ill-conditioned as $\mu \to 0$ - Needs $LDL^\top$ with pivoting and the **inertia** $(n, m, 0)$ to choose $\delta_w$ - Most of the time, and most of the difficulty, is in this solve </div> <div> - **Bonus:** at the solution, the factored KKT matrix gives $\partial x^*/\partial p$ with one back-solve per parameter (sIPOPT) - That is what makes the **solver differentiable** </div> </div> scimax-hidden

Be careful with this audience: the profile is on our own harness of ~1,200 problems, against Ipopt with MA57. It is evidence the port is solid, not a claim of beating mature commercial solvers. Feral's job is the KKT solve plus a trustworthy inertia count. Try it: jkitchin.github.io/pounce/demo (drop an .nl file, solved client-side).

X_RC,i = d ln r / d ln k_i at fixed K_i (Campbell). PO desorption limited (step 14, +0.99), O2 poisoned (step 17, -0.91). The point for this audience: the solver is a differentiable layer, so a model built once serves estimation, sensitivity and design.

This is the part of the landscape where this audience (MINOTAUR, filterSQP) knows far more than I do. I would value your critique. discopt is broad because agents make breadth cheap; depth and robustness still come from benchmarks (MINLPLib, QPLIB, CUTEst). David Bernal contributed major global optimization pieces.

Hover a model for what it is and how it gets its uncertainty. Four regions: symbolic grove (jaxsr, iBART, SISSO), decision forest (linear/hyperplane trees, soft trees), neural meadow (ICNN, monotonic, periodic, KAN, LLPR, DPOSE), and distributions (flows). Written version: kitchingroup.cheme.cmu.edu/posts/differentiable-surrogate-zoo

scimax-hidden ## Uncertainty drives the next experiment <div class="cols"> <div class="side"> $$ q(P) = \frac{q_{\max} K P}{1 + K P} $$ - Low-pressure data only determine the lumped $q_{\max} K$ - Every curve in the 95% region fits the data equally well - The **Fisher information** from the solver says where to measure next  </div> <div class="center">   **Before: very uncertain. After: very confident.** </div> </div> <!-- Same machinery as the DRC slide: sensitivities of a solved model. This is the bridge to the lab: design of experiments is an optimization problem over a differentiable model. -\-> scimax-hidden

This is the experiment-planning engine in the MFI loop. The agent reads the workbook, fits, proposes the next runs, and the human approves. Browser app (Pyodide, nothing leaves your machine): jkitchin.github.io/discopt-doe/app/ -- good for teaching too.