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fixed several typos

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N_T 2025-08-06 15:08:15 +02:00
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2
intro.md
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@ -15,7 +15,7 @@ We are living in an era of rapid transformation. These methods have the potentia
```{note} ```{note}
_What's new in v0.3?_ _What's new in v0.3?_
This latest edition takes things even further with a major new chapter on generative modeling, covering cutting-edge techniques like denoising, flow-matching, autoregressive learning, physics-integrated constraints, and diffusion-based graph networks. We've also introduced a dedicated section on neural architectures specifically designed for physics simulations. All code examples have been updated to leverage the latest frameworks. This latest edition adds a major new chapter on generative modeling, covering powerful techniques like denoising, flow-matching, autoregressive learning, physics-integrated constraints, and diffusion-based graph networks. We've also introduced a dedicated section on neural architectures specifically designed for physics simulations. All code examples have been updated to leverage the latest frameworks.
``` ```
--- ---

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overview-optconv.md
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@ -62,7 +62,7 @@ In several instances we'll make use of the fundamental theorem of calculus, repe
$$f(x+\Delta) = f(x) + \int_0^1 \text{d}s ~ f'(x+s \Delta) \Delta \ . $$ $$f(x+\Delta) = f(x) + \int_0^1 \text{d}s ~ f'(x+s \Delta) \Delta \ . $$
In addition, we'll make use of Lipschitz-continuity with constant $\mathcal L$: In addition, we'll make use of Lipschitz-continuity with constant $\mathcal L$:
$|f(x+\Delta) + f(x)|\le \mathcal L \Delta$, and the well-known Cauchy-Schwartz inequality: $|f(x+\Delta) - f(x)|\le \mathcal L \Delta$, and the well-known Cauchy-Schwartz inequality:
$ u^T v \le |u| \cdot |v| $. $ u^T v \le |u| \cdot |v| $.
## Newton's method ## Newton's method

2
probmodels-diffusion.ipynb
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@ -31,7 +31,7 @@
"Given a data point $x_0$, we can sample the noisy latent state $x_t$ from the forward Markov chain via\n", "Given a data point $x_0$, we can sample the noisy latent state $x_t$ from the forward Markov chain via\n",
"\n", "\n",
"$$\n", "$$\n",
" q(x_t|x_0) = \\mathcal{N}(x_t, \\sqrt{\\overline{\\alpha}_t}x_0, (1-\\overline{\\alpha}_t)I)) ,\n", " q(x_t|x_0) = \\mathcal{N}(\\sqrt{\\overline{\\alpha}_t}x_0, (1-\\overline{\\alpha}_t)I)) ,\n",
"$$\n", "$$\n",
"\n", "\n",
"with the inverted weights $\\alpha_t = 1 - \\beta_t$ and alphas accumulated for time $t$ denoted by\n", "with the inverted weights $\\alpha_t = 1 - \\beta_t$ and alphas accumulated for time $t$ denoted by\n",

8
references.bib
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@ -13,6 +13,14 @@
@STRING{NeurIPS = "Advances in Neural Information Processing Systems"} @STRING{NeurIPS = "Advances in Neural Information Processing Systems"}
@article{braun2025msbg,
title ={{Adaptive Phase-Field-FLIP for Very Large Scale Two-Phase Fluid Simulation}},
author = {Braun, Bernhard and Bender, Jan and Thuerey, Nils},
journal = {{ACM} Transaction on Graphics},
volume = {44 (3)},
year = {2025},
publisher = {ACM},
}
@inproceedings{lino2025dgn, @inproceedings{lino2025dgn,
title={Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks}, title={Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks},